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Fyllt Mendelsen a Neffron Barofsky, Llywodraeth Cymru, Ruth Kennedy of the Centre for Scotland and Israel Relations, and many other friends and members from the Jewish community in Scotland, many of whom are visiting Holyrood for the first time today. I want you to know that you are very welcome here today in Scotland's Parliament. I am also delighted to be moving a constructive and positive motion in support of Scotland's Jewish community directly concerning our approach to Israel. I do so against a background in which it is easy to understand why many in the Jewish community have become deeply concerned about their devolved Parliament, Scotland's devolved Parliament, having tabled some 371 motions in foreign countries with 62 of them concerning Israel and 36 of those being strongly condemnatory, and to this I'll return. I start with an unapologetic why. Why move today's debate at all? I grew up in Newton Merns in the East Renfisher, a southern residential suburb of Glasgow. The late Ralph Glacer in his extraordinary biographical quadrilogy, which began with growing up in the Gorbells, tells the story of Jewish migration to Scotland and Glasgow at the start of the last century and how in the post-war years many in the Jewish community migrated from Glasgow to East Renfisher quickly becoming a significant population. The next door to me were the Maples family, next to them the Greens, across the road from them were the Davidsons and the Cones, along the road from them were the Marcos and the Cline glasses, across the street with the roses, the fells and the tunes. Yes, to me, having Jewish families in my community was an everyday part of my life. They were my friends and my neighbours. Yet a community of some 47,000 families just after the Second World War is now probably just some 20 to 30 per cent of that today. In addition, and not at all well understood, Scotland is also home to a separatist really community of some 1,000. All of this is important because the feeling of alienation, of isolation, of vulnerability felt by many in these communities to the point where significant numbers are saying for the first time that they are considering leaving Scotland is born in part out of a casual ignorance of the community that is expressed in many parts of Scotland. I am a proud Glaswegian, proud to be Scottish and British too. Do I support everything ever said or done in Glasgow or Scotland or the UK's name? Of course not, but do I then equate differences that I may have with any particular city or country, with the people of that city or country? No, I do not. Yet, Presiding Officer, in Scotland too many of articulated slogans and narrow partisan campaigning tactics against Israel to such an extent and occasionally in such a manner as to stray albeit sometimes inadvertently, although sometimes deliberately, into the language of anti-Semitism. Some overtly personally blame the Jews, a term in that context used pejoratively, for the actions of a foreign government while seemingly questioning the right of Israel to exist at all. This is all the more disturbing when you appreciate that the UK Jewish community has a very strong attachment to the state of Israel. A 2010 survey by the Institute of Jewish Policy Research showed that an extraordinary 95 per cent of UK Jews have visited Israel and 90 per cent view Israel as the ancestral home of the Jewish people. I gladly applaud the direct intervention of the First Minister who recently said that there is nothing that happens in Israel or Palestine that can be a justification for anti-Semitism or any racial or religious hatred—a point that has been made very strongly at every level of Scottish society. My motion advocates a different and supports a different course. For beyond the conflicts, Israel is a great nation that will celebrate its 68th independence day this year. Since 2004, Israeli scientists have won five Nobel prizes, a tally only bettered by four other nations. Between them, Israeli scientists and others produced some 16,000 key technical journals more than the entire Arab world combined. Israel is a country of invention. Last year in the US, Israelis lodged some 1,900 patents just below two nations of far greater populations. Among those, Israel is number one in the world for medical device patents and biotechnology patents per capita. Among the other inventions that we use every day is the US B flash drive—how inconvenient to many if we were all to boycott that. In recent years, the BDS has become an aggressive and strident opponent. It has thought nothing of bold intimidation and disruption, which has led to the cancellation of events involving Israeli artists or benefiting from Israeli sponsorship in Scotland, as seen, for example, at the Edinburgh festival fringe in 2014. That has carried beyond, particularly among an impressionable youth, on to the campuses of some of our great universities. More than once and increasingly more often, I am hearing first hand of distressed Jewish students who have been directly targeted personally or had events disrupted. What does that really achieve? What consequences could follow? By way of illustration, I touched on two specific cultural activities in Scotland. The Aberdeen International Youth Festival has enjoyed a biannual visit from the Israeli Kyriat Ono Youth Concert Band. Its conductor, Guy Fedder, said that if we were stopped from coming, it would break the very essence of what we aim for. Music is a universal language. It crosses borders and creates bridges. It is a field in which we can overcome our daily disagreements and do something beautiful together. Or this month, as his exhibition ends at the National Portrait Gallery here in Edinburgh, Matan Ben Kenan, winner of the BP Portrait Award 2015. As I see it, he says, the majority affected by the boycott are individuals, artists, scholars, scientists, most of whom are private people who do not represent any political authority but represent a variety of political thoughts and views. My motion today is expressly about the benefits to peace and understanding of cultural bridges, not boycotts. That duty requires us to be responsible. A seeming obsession with tradducing Israel and its very right to exist and the unthinking conflation of Israel and the Jews undermines the security and wellbeing of Jewish people in Scotland. Antisemitism is not only the abuse of Jewish individuals but treating Jewish organisations, including the Jewish state, differently from others. I understand and have heard directly the aspirations of Palestinians, and I am not today seeking to pretend that this debate can solve a conflict that has defied the ages. But I do recognise Israel as the one genuine parliamentary democracy in the region, and I celebrate that fact. There is clearly room for legitimate and passionate debate, but Scotland's role should be consistent with our traditions and ambitions. Our democracy must be an example of reasoned, well-informed argument in debate. We should not allow ourselves to shut down democracy, to shout down one side, to shout down democracy. I started with my own experience growing up in Newton-Mernes and of my childhood friends and neighbours. It is a small world. All these years later, I find that one of my sons has been stepping out to use an old-fashioned idiom for some five years now with the daughter of one of those very Jewish friends who lived across the street. I am proud that this is possible in Scotland. As the First Minister said, I do not want to be the First Minister or even live in a country where Jewish people want to leave or hide their identity. This Parliament's record of acknowledging the Holocaust annually is a deservedly proud one, but that must never become simply a box-ticking annual exercise leaving any one of us free to talk pejoratively the rest of the year about Israel or to allow ourselves or ignorance to become a cover for antisemitism. In that context, I think a refreshing of our approach to Israel is overdue. Let us reach out and through cultural exchange and debate demonstrate what we can achieve and what boycotts and antisemitism cannot. Many thanks. Before I call on Stuart Maxwell to be followed by John Finnie, I would just like to ask members in view of the number of members wishing to speak in today's debate. I am minded to accept a motion under rule 8.14.3 to extend the debate by up to 30 minutes. Would you move that motion, Mr Carlaw, please? So the question is, are we minded to extend this debate in these circumstances? We are. Many thanks. I now call on Stuart Maxwell to be followed by John Finnie. Four minutes, please, or thereby. I would like to begin by congratulating Jackson Carlaw on securing time for a debate on this very important subject. The Israeli-Palestinian conflict is a very difficult and fraught subject and feelings obviously run very high. It is natural that people should look for a way to help in this very painful division. Of course, a cultural boycott is a way of bringing moral rather than physical pressure to bear. Certainly, there is nothing to stop any one of us from choosing where we spend our money. We may certainly choose not to buy certain products, nor to attend certain events, and no one can stop us. That is our right. People are free to choose, and I support that freedom to choose. It is also our right to try and persuade other people that our view is the correct one, to try and win others over to our way of seeing the situation. However, here I have to express a concern about the way that this call for a cultural boycott is being pressed forward. It seems to me that what is being called for here is not just for individuals to exercise their consciences, but for a refusal to allow other people to make a different decision, and I have to confess that that worries me. For example, in 2012, the Bachiva dance group was picketed at the Edinburgh festival, and that is the right of individuals in a free society to make their feelings known to those attending the event, and I would certainly support the right of individuals and of groups to pick it outside performances. That is the mark of a healthy in a free society where different opinions can be expressed. However, that performance inside the hall was disrupted by protesting individuals. That, to my mind, went too far. It is one thing to engage with people attending a performance and suggest to them that they should not do so. It is quite another to impose your point of view on all those who take a different point of view and have chosen to attend. That is not discussion, nor is it debate. It is an attempt to shut down discussion, to silence those that you disagree with, and I do not support that. The Palestinian-Israeli conflict, as well as being long-standing and painful, is nuanced. That is, like most of life, not a black and white situation. There is no doubt that many Palestinians suffer greatly, but so do Israelis. Not just from rockets fired into civilian areas or suicide bombers and buses, but from the recent spate of knife attacks and car rammings that have occurred in Israel. People, innocent people on both sides, suffer. If we wish for a peaceful solution, which I know we all do, we cannot ignore the feelings evoked by the suffering on both sides. We cannot afford to silence one of the voices in this tragic situation. I do not believe that that will lead to peace in the long term. The cultural world, too, is divided over the subject of a boycott of Israeli institutions and organisations that are funded by Israeli institutions. Some artists are greatly in favour of a boycott, and some artists are strongly against it. One thing that concerns me about the discussions on the conflict is the underlying feeling that there is bad faith on the part of those who do not wish to support a cultural boycott of Israeli artists, poets and actors. I do not think that there is anyone in this Parliament who does not believe and believes strongly in the two-state solution for Israel and Palestine, with both states being thriving democracies with three citizens living in peace and harmony with each other and the rest of the world. That is what I know we all hope for. We may disagree on the route, but the hope for destination is the same for all of us. I firmly believe that the best way to secure that long for peace is to keep open as many avenues for engagement and dialogue as possible. Cultural events are one way of doing that. Before I call Ken Macintosh, could I ask for the public's help in that there should be no audience participation in the proceedings of Parliament? Thank you for your consideration of that matter. I now call on Mr Ken Macintosh to be followed by John Mason. John Finnie to be followed by Ken Macintosh. Many thanks, Presiding Officer. I apologise to you and Mr Carlin in advance that, because of another committee engagement that I have at 1.15 the Police Committee, I may have to leave before the end of the debate. I would also like to declare my membership of the Scottish Palestinian Solidarity campaign and the Scottish Green Party. The Scottish Green Party's mantle is people, planet and peace. Peace and security can only be achieved through global justice, and the world will never be safe where we allow the obscenity of poverty to continue, for instance, while economic exploitation and illegal occupations continue. Turning to the issue of boycott, divestment and sanctions, Mr Carlin's motions are misleading. There is no boycott of Israeli artists such as Matt and Ben Gran, so long as artists refuse to collude in Israeli abuses of human rights, there is a boycott of the Israeli state and those who seek to normalise the occupation of Palestine. The Scottish Green Party supports Palestinian's call for boycott, divestment and sanctions against Israel, including a boycott of Israeli goods and services, and an academic and cultural boycott until Israel fulfills its obligations under international law. Let me tell you what those obligations are. They are with drawing to the pre-1967 border, with drawing from East Jerusalem, the Golan Heights and other lands seized in 1967, with drawing from and depopulating Israeli colonies in the West Bank, dismantling the separation wall and ending the siege of Gaza, granting the right of refugees for 1948, 1967 and other expulsions and their descendants to return to their homes, as required by UN Resolution 194. Affording equal rights to all citizens with it at Israel, irrespective of religion or ethnicity, and I have to say, speaking like this and then being accused of being anti-Semitic, I have no allegiance to any faith nor would I be critical of any faith, and especially granting full rights to Palestinian citizens of Israel. The Scottish Green Party will continue to campaign for and support divestment by local authorities, other institutions of government, including the local government pension scheme and civil society organisations from Israel, Israeli companies and companies supporting the Israeli Government's illegal occupation of Palestine. The Scottish Green Party supports Palestinian non-violent struggle for resistance to the colonisation of their lands, resources and people by Israel and by Zionist settlers. The Scottish Green Party will press for EU legislation to prohibit the import into the EU of products from Israeli settlements in the West Bank. The Scottish Green Party will work with solidarity groups within Scotland and political parties and civil organisations within Palestine and among the Palestinian diaspora who share those objectives. The motion talks of culture of coexistence and you cannot have that when you have apartheid walls. Talks of greater understanding, but is there an understanding of an imprisoned population? Talks of peace through cultural engagement. I love peace, I campaign for peace, I encourage peace, I condemn violence from whatever quarter and I hope that all other participants in this debate would be likewise. I want to encourage equality. I support conflict resolution, but peace came in the north of Ireland, not when walls went up but when the walls came down. I spoke to someone involved in violence in the north of Ireland and he said, you know, we killed each other, we maimed each other, we injured each other, we damaged each other's property. Nothing changed until the bomb of the city of London. Now, I'm not condoning violence from any quarter, be that violent against individuals or violence against property, but there is no doubt that financial imperative can shape minds and can change opinions, so I'm full square behind the boycott divestment and sanctions. Many thanks. I now call on Ken Macintosh to be followed by John Mason. Four minutes on thereby please. Thank you, Presiding Officer, and can I begin by offering my thanks to Jackson Carlaw for securing today's member's debate. Given the disproportionate number of anti-Israeli motions laid in this Parliament, we may not redress that balance today, but I do hope that we show that Scotland is not universally hostile to the state of Israel, that we recognise the incredibly difficult task of securing peace in the Middle East, and that we demonstrate our own commitment to ethnic and religious tolerance, to cultural understanding and to supporting our own Jewish community here in Scotland, and I too will return to that last point in my concluding remarks. Presiding Officer, I don't pretend to be an expert on Israel, and I do consider myself to be a fair-minded person. I particularly consider myself to be sympathetic to those who are suffering in any way, and I would defend the right of any Scot to speak up for the Palestinian people and to plead their cause. But at some point over recent years, support here in Scotland for the plight of the Palestinians has turned into hostility against Israel, that I believe is one-sided, inaccurate and, in the end, incredibly unhelpful and damaging for all concerned. Those who support the boycott divestment and sanctions campaign constantly refer to Israel as an apartheid state, a description that is as unfair to the struggle of the anti-apartheid movement as it is to those Israelis who fight to defend democracy, freedom of expression and the rule of law. I wonder if many of us can imagine what it is like to wake up every morning in a country surrounded by neighbours who do not recognise your right to exist or where many are pledged to obliterate you. Despite that, in Israel, human rights are protected, and Arabs, Jews, Christians and Druze alike are elected to Parliament, serving the army and hold high legal office. In some countries nearby, women are not allowed even to drive unaccompanied.  Yet Israel, almost alone in the region, opposes all forms of racial segregation and insists on equal rights for all, whatever their gender or sexuality. I do not recognise that as an apartheid in any way. To lay the blame on Israel for everything that is wrong in the Middle East strikes me as blinkered, unbalanced and unlikely to lead to the successful and sustainable peace that I hope we all desire. Frankly, I did not want to contribute today because I felt a need to share my own views on Israel. I want to speak up because I believe that Scotland's growing hostility for Israel has created an atmosphere of anxiety among many members of the Jewish community in Scotland that is deeply troubling for all of us who believe in a tolerant, inclusive and caring multicultural society. I recognise that many of my parliamentary colleagues do care deeply and passionately about the Middle East and hold very strong views about the situation in Israel and Palestine. I will be honest that, given that foreign affairs are predominantly reserved to Westminster, I have misgivings about debating such issues here. It is easy to express our views on issues where we are not held accountable. That, in turn, can lead to irresponsibility. I do not wish this Parliament itself to be reduced to a talking shop. However, anti-Israeli sentiment is now in danger of becoming rooted in civic Scotland. In some academic circles, among some trade unionists, it is almost a totemic issue for some of my colleagues on the left. I worry that here in the Scottish Parliament MSPs have played a part in that process.  The result has been to shake the confidence of families who have lived here for generations. The research that is recently carried out by the Scottish Council for Jewish Communities revealed people feeling isolated and vulnerable, with many thinking about leaving their own country, their own home, Scotland, for good. Over the years, as an MSP, I have tried various ways to address, in fact, to redress, this growing prejudice and the resultant anxiety. Sponsoring an exhibition on Israel's phenomenal contribution to the modern world, hosting speakers to talk about the reality of day-to-day life in Israel—for example, equal access to medicine—unfortunately, the reaction to those events has often been expressed through the very behaviour that I am so keen to counter—depressingly illiberal attempts to interrupt, disrupt or shout down discussion. Is that really what we have become? A harsh, unwelcoming, intolerant country, more interested in preventing concerts or banning books than in spreading understanding? That is not my vision for the modern Scotland. I urge all colleagues to think again about how we change views and attitudes, not through condemnation but through discourse, learning and engagement. Let's start today, right here in the Scottish Parliament, by building bridges. Thank you very much. We now call on John Mason to be followed by Alison Johnstone, four minutes or thereby. Thank you to Jackson Carlaw for bringing this debate today. We have debated Israel and Palestine before, and I am happy that we do so again today. My theme is probably going to be similar to what I have said before here, namely that we should be encouraging peace talks, we should be trying to reduce tension and we should not be cheering on either side. I would not describe myself as a pacifist, but the more I read about the events 100 years ago during World War I, the less I believe that violence and war solve very much at all. Those sympathetic to Israel are positive about today's motion in contrast to past motions that were seen as very anti-Israel. I have had a number of emails thanking me for supporting the motion, but those emails have also thanked me for supporting Israel. I guess that it depends on what you mean by support. The picture that comes to my mind is of a football supporter cheering on their team through thick and thin, no matter what. I have to say that I have written back to those correspondence to say that I do not support either Israel or Palestine in that sense. What I do support is a two-state solution, and I think that a lot of fair-minded people on both sides say that they support that. Is it actually achievable, or does the history since 1948 show that, frankly, it is impossible? You can call me naive if you want, but I believe that it is achievable if there is the international will to do it. There are a lot of big regional and world powers that need to be around that table—Iran, Saudi Arabia, Egypt, Russia and the United States—for starters. Between them, I believe that they are able to pressurise both Israel and Palestine to take part and to take part meaningfully in a peace dialogue. After all, the reality is that both Israel and Palestine are pretty small in the scheme of things. If we could agree that that is the way ahead, then it seems to me that cheering on either side will not help, cultural, sport and other boycotts will not help, and certainly supplying excessive amount of arms will not help. My next point would be to ask why Israel is singled out for so much hatred. It is repeatedly accused of war crimes, apartheid, occupation, murder and countless other horrors. Yet a number of other states on the international scene have almost certainly worse records. Amnesty International's recent report for 2015-16 speaks about China and its record on Tibet, on religion and on human rights. Saudi Arabia, which uses the death penalty extensively with women facing discrimination and severe restriction on freedom of expression, or Egypt, where thousands are arrested even peaceful critics. Why is Israel singled out for so much opposition? It would be more understandable if there were also calls to boycott China and Pakistan for their human rights records. I wonder if it is because firstly Israel is so small and secondly Israel is Jewish. I am regularly told by folk that they are critical of Israel but are not anti-Semitic or anti-Jewish. I can understand that as I would also consider myself critical of North Korea, for example, but I am not, I hope, anti-Korean. However, I do feel that for some people at least a justifiable criticism of Israel switches over to a real hatred. We in Europe have to be very careful about this because we in Europe have a joint history of being very anti-Jewish. That has run for hundreds of years and culminated in the 1940s, but are we certain that it finished in the 1940s? Jews in Glasgow find themselves being blamed for the faults of Israel today. All I ask from today is that we do all that we can to build bridges, both within Scotland and internationally, and I believe that both Scotland and the UK have a role to play in bringing peace in the Middle East. Thank you. Thank you very much. I now call on Alison Johnstone to be followed by Claudia Beamish. The Scottish Green Party supports the boycott, divestment and sanctions campaign because it is a very effective tool for supporting the Palestinian people and their struggle against oppression. There has long been an international failure to hold Israeli governments to account for disregarding international law and ignoring the health, safety and human rights of Palestinians. As the Palestinian Solidarity campaign highlights, the 2005 call for boycott came from leading Palestinian cultural and academic figures who urged their counterparts in civil society and people of conscience all over the world to undertake initiatives against Israel similar to those applied to South Africa in the apartheid era. By putting economic pressure on the Israeli Government, we can join a worldwide campaign calling on corporations who are profiting from Israel's occupation of Palestinian territories to pool their funding. Boycott is a legitimate form of protest, but of course it is one that we do not undertake lightly. As my colleague John Wilson points out in his motion opposing restrictions on the right to protest, similar campaigns help to weaken the apartheid regime in South Africa. As has been said already by my colleague John Finnie, this is not a boycott against Israeli artists who are not being used to support brand Israel, the Israeli propaganda strategy designed to whitewash human rights abuses. There is a boycott of the Israeli state and those who seek to normalise the occupation of Palestine. I think that it is important that we understand that a deep and unwavering commitment that none of us should ever forget or downplay the atrocities of the Holocaust and the oppression of the Jewish people is entirely consistent with opposing any abusive actions by the Israeli Government or indeed any Government and to argue otherwise obscures the genuine attempts of those who want to see a secure and lasting peace in the Middle East and who believe that the biggest obstacle to achieving this is oppressive Israeli state action. Mr Carlaw in his motion suggests that we should pursue greater cultural links with Israel rather than boycotts that make clear that Israel's treatment of the Palestinian people is unacceptable. However, to do so while the oppression of Palestinians continues would be to sweep under the carpet the Israeli attacks on Palestinian culture including vandalism, destruction, closure and military attacks on Palestinian cinemas and theatres, the banning of cultural events and restrictions on the movements of Palestinian artists. It is truly alarming that still in this day and age it is impossible to express solidarity for desperate and oppressed people without facing accusations of bigotry against their oppressor. I do not agree with Mr McIntosh and Mr Carlaw that there is growing hostility against Israel. Absolutely every person on this planet is entitled to a peaceful existence here in Scotland globally and I want to work with all parties who can contribute to the end of the occupation of Palestine by non-military means. A just peace in Israel and Palestine could be the catalyst for achieving wider peace in the region and across the world and efforts to criminalise boycotts or publicly smear those who express support for the Palestinian people can serve only to hinder any progress towards peace. We have the choice of following those such as Archbishop Desmond Tutu, who fought to end South African apartheid and supports the BDS campaign or failing to play any part in efforts to end this apartheid in the Middle East. Presiding Officer, the cultural boycott of Israel is moderate in its objective simply to ensure that Israel observes international humanitarian law. Thank you. Thank you very much. I now call on Claudia Beamish to be followed by Sandra White. Thank you Presiding Officer. I'd like to declare an interest in that I'm a convener of the cross-party group for Palestine. I'd also like to thank Jackson Carlaw for enabling the opportunity for this very complex and difficult issue of peace for the Palestinians and for Israel and for recognition also of the importance of making sure that there is no anti-Semitism here in Scotland today to be brought to the chamber. I thank him for that. I want to start by making it clear that I have bore any anti-Semitism or any racism of any kind. If we are to reach a just and peaceful solution for Israel and for Palestine and for the Middle East, I'm clear that we need some cultural bridges and boycotts. One such cultural link to be welcomed, which I've highlighted in a previous speech in this chamber about this complex issue, is to be found in the West Eastern Divan Orchestra, founded by Daniel Barenboin and Edward Said. It's one initiative, the aim of the orchestra of which I quote is to promote understanding between Israelis and Palestinians and pave the way for a peaceful and fair solution of the Arab-Israeli conflict. Through such cultural links, young people in Israel can surely start to understand the real state of affairs. However, there are strong reasons to consider the boycott of some events if they are connected with the oppression of the Palestinian people by the Israeli state. I heard of an initiative recently whereby young Israelis and Palestinians were playing in the same football team, being promoted as a good story. This is indeed a good story, but, Presiding Officer, we need somewhat of a reality check here as well, because what we need to remember is that Israel is an occupying state and the Palestinians live in occupied territories. I have been to Gaza with the Council for European Palestinian Relations. My father was a soldier in Bethlehem, a regular soldier before the last world war, and I grew up with Palestinian exiles. It is just to highlight that, when my colleague John Finney and I went to Gaza, it was in November 2012, very soon after the Operation Pillar of Defence. We saw with our own eyes the effect of disproportionate force. While I in no way condone any violence of any kind and I do not believe that this is the solution going forward, I want to stress that we saw with our own eyes the effects of this force and the destruction and mayhem caused a civil society. Cultural links in my belief are not enough for a just solution. We need to act on boycott, divestment and sanctions, BDS. As my colleague Alison Johnson said, Palestinian society in 2015 and now with over 300 organisations has set up this initiative. In my view, I believe that this is a powerful tool for people around the world to play their role in standing up for struggling Palestinians. The Israeli state has simply, in my view, disagreed with the numerous rulings of the international law that state that their settlements are illegal and continues to deny Palestinians fundamental rights of freedom, self-determination and equality. The past holds significant examples of power of the effective boycotts. Rosa Parks' bravery triggered a boycott that began with a bus company and was part of the civil rights movement in America. Of course, the apartheid regime in South Africa was bought to its knees in part thanks to the global solidarity against the South African industry, academia and culture. Today, I welcome those in the gallery and I welcome the Israeli representatives in the gallery above us here. I hope that they will take back the concerns and views that I have highlighted, which many in Scotland support in the hope that not only will there be a lasting peace, but it will be a just peace for the people of Palestine, which will also make sure that there is security in Israel and in the wider Middle East. Thank you so much. I thank Jackson Carlaw for bringing this debate to the chamber and I welcome all those in the public gallery who are here in attendance today. As a motion states, the Parliament acknowledges the recently published open letter, signed by over 150 high-profile cultural and political figures in support of the aims of culture for co-existence, calling for an end to cultural boycotts. That was published in the Guardian in October 2015. The Parliament should also acknowledge that this opinion is in response to a letter signed by hundreds of artists published in the Guardian in February 2015 expressing the opposite. That, Presiding Officer, is their choice. The freedom to express their beliefs and opinions and respect their right to have that freedom and I will defend those rights. That is why many people, myself and others included, are very concerned by attempts to limit local authorities, autonomy and people's rights to protest, which is coming from the Westminster Government. As individuals and communities and societies, those freedoms are what define us, to form the fundamental basis of our democracies and are rightfully cherished. Jackson Carlaw has brought this debate forward today in our Parliament and this is a perfect example of these rights. Opinions may differ, they may not be agreement but they are not to be denied. In fact, these opinions and the difference in them are to my mind what will hopefully drive us towards a peaceful solution to the situation we are faced with and the resolution also. I do not believe that by silencing these voices, peace will be achieved and I believe that that is something which we, all of us, must remain mindful of. There are many people on both sides who have spoken to in both communities who I know want to see a just and lasting peace and this is where our energies and efforts should and can achieve real results. Yes, they may not agree, in fact they may disagree on how to achieve it if they are united in the desire for peace. However, we can work towards peace in these two areas and we must, for the sake of the Palestinians and the Israelis, work towards a just peace for all of the peoples in this area in the Middle East. I mentioned earlier that we may disagree on how this is achievable but there is a desire there, Presiding Officer. I know that there is a desire there from both sides and I know that we can agree on something and that gives me optimism that it can be achieved but it will not be achieved by silencing people and denying them the right of protest. I want to thank Stuart Maxwell for his very measured contribution today. I think that it does him great justice. Also, Alison Johnstone for her excellent contribution which encapsulated the thoughts which many people have, the thoughts of many and also the contributions for other contributors and my colleagues here today. To conclude, Presiding Officer, I once again thank Jackson Carlaw for bringing this debate to the chamber for her respect and his right to put across his opinion and to act upon that. As individuals, we have a fundamental right to opinion and expression and that should be respected. Thank you. I now call on Jeane Irker, after which I will move to the closing speech from the cabinet secretary. I, too, must begin by thanking Jackson Carlaw for bringing this debate to the chamber today. I declare an interest. I am a member of the cross-party group for Palestine and a member of the Scottish-Palestinian Solidarity campaign. I challenge Jackson Carlaw and his remark about anti-Semitism. Many thousands of others are critical of the Israeli Government and are sympathetic to Palestinians, but who are not anti-Semitic does not make us anti-Semitic. I have lived and worked in Scotland most of my adult life and have worked on more than one occasion with Jewish people. If I have one thing that I want everybody to remember today that any political opinion and criticism of the Israeli Government does not equate with anti-Semitism. Let's look at what the artists are saying in the United Kingdom and the current pledge to support this boycott from Scottish artists. We support the Palestinian struggle for freedom, justice and equality. In response to the call from Palestinian artists and cultural workers for a cultural boycott of Israel, we pledge to accept that are professional invitations to Israel, nor funding from any institutions linked to its Government until it complies with international law and the universal principles of human rights. Let's look, too, at some of the cultural events that have happened. I am not... forgive me if I mispronounce, but Airy Mechel is really foreign ministry. We will send well-known novelists and writers overseas, theatre companies, exhibits. This way, you show Israel's prettier face so we are not sort of purely in the context of war. But let's look at some of the facts of Israel's attacks on Palestinian culture. In 87, Israeli authorities closed the cinema in East Jerusalem. The theatre remained closed until Palestinians reopened it in February 2012. In 2002, Israel prevented Palestinian poets, Zachariah Muhammad and Chassan Zaktan, from travelling to Ireland to read their work. In 2002, Israeli soldiers in Bethlehem vandalised a theatre and destroyed equipment. In May 2009, Israeli soldiers prevented the opening of the Palestine festival of literature in Jerusalem. In 2009, the Israeli authorities banned numerous Palestinian cultural and educational events scheduled to celebrate the declaration of Jerusalem as the capital of Arab culture for that year. I would say, Presiding Officer, that we have to recognise some of the investment of our own artists in their declaration to support this boycott. The late Ian Banks, who was noted in this chamber and supported by everyone as the intellectual that he was and the creative writer that he was, refused to allow his books to be published in Israel. He said that the BDS campaign for justice for the Palestinian people is one that I would hope that any decent, open-minded person would support. Gentile or due, conservative or leftist, no matter who you are or how you see yourself, these people are our people. Collectively, we have turned our backs on their suffering for far too long. Presiding Officer, I hope today that we reassure the large number of people in this chamber who are in the public gallery that this is not anti-Jewish sentiment but rather one of international law and human rights. Thank you. Thank you very much. I now call on the Cabinet Secretary if you want to his lip to wind up the debate on behalf of the Government. Seven minutes or thereby please, cabinet secretary. First of all, I congratulate Jackson Carlaw on securing this debate and the range of different positions of members that should be articulated well-argued, strongly argued and considered speeches from across the chamber. Jackson's carlers motion concerns the open letter signed by the supporters of the culture for coexistence network. I note that the chair of culture for coexistence Lorraine Dacosta stated that that culture has a unique ability to bring people together and bridge division. In general policy terms, the Scottish Government recognises and supports artistic freedom and the role that culture plays to increase understanding of others. In line with other Governments in Europe and indeed Mahmood Abbas, President of the Palestinian National Authority, the Scottish Government does not advocate a policy of boycotting issue. Any engagement with the Israeli Government or the Palestinian Authority provides us with an opportunity to call for a peaceful resolution between both sides of the conflict and to put forward our concerns in the strongest possible terms that we do at each and every opportunity. The Scottish Government has also made it clear on a number of occasions that we do not dictate to cultural institutions, organisations or individuals what approach they should take. The Scottish Government strongly encourages the Israeli Government and the Palestinian Authority to work with the international community on securing long-term peace and ending the cycle of violence that continues to affect both Palestinians and Israelis. The Scottish Government supports the EU position of a two-state solution based on the 1967 borders and firmly encourages both Israel and Palestine to reach a sustainable negotiated settlement under international law, which has at its foundation mutual recognition and determination to coexist peacefully. We aspire for Scotland to act as our good global citizens and drawing on our own experience at home to promote tolerance and respect for human rights in other countries. Whenever the question of Israel and Palestine is raised in this chamber, we consistently urge all sides to seek a peaceful negotiated solution that respects the rights of all the communities affected. By the same token, we have consistently condemned obstacles to progress in the peace process, likely in the discriminate rocket attacks on Israel or the continued expansion of illegal settlements in the occupied territories. We have also repeatedly called on the UK Government to use its influence to help to revitalise the peace process, finding a way to break through the political deadlock and bring an end to the conflict. Within Scotland, the Scottish Government does not tolerate violence or extremism in any form and we condemn it when directed at any of our communities, whether in deed or word. Jackson Carlaw is correct in stressing the need to support all of our minority communities in Scotland. We absolutely support that, but he is wrong in saying that criticism of Israel means that you are anti-Semitic. I think that that point was made by Jeane Arquett. I think that he was very careful not to say that. I said that unfortunately, inadvertently, on occasion, and I regrettably, sometimes deliberately, one is used to being the other, but I do not, as for a moment, suggest that that is universally and always the case. I think that that is a very important clarification and very important in the context of this debate. The free and open exchange of ideas is vital in building understanding and trust between communities. We want to encourage an environment in Scotland where those kinds of conversations can take place. Our former First Minister wrote to Israeli Ambassador Todd back in December 2012 to underline Scotland's value and commitment to cultural freedom and our encouragement of recent debate. Culture from Israeli artists features regularly as part of our festivals and tours in Scotland. Jackson Carlaw mentioned the Aberdeen International Youth Festival, which I have attended, and at no point has the Scottish Government intervened in the artistic creativity and integrity of Scottish programmers who have invited those artists to form part of their programme. Culture has become a powerful tool to promote dialogue and debate, to help to promote a better and deeper understanding of other nations, which can help the process of resolution in the areas of conflict. Across Scotland, our culture sector is leading the way in these debates, bringing international delegates from regions such as Iran, Iraq, Israel, Palestine and many more to be exposed to our culture and to build a relationship of trust. One example of an attempt to break down borders was the theatrical company Northern Stage, who worked with Scottish playwright David Gregg, who, to host their show, hears the news from over there at the Edinburgh Fringe in 2015. It had 20 writers from across the Middle East contributing stories, poems and reportages via Twitter that has flashened into theatrical cabaret with different content each night. The host included Sarah Sharrawe from Egypt, Hassan Abdul-Razik from Iraq and Lebanese writer Alwagie. Culture builds bridges to enable dialogue between people as individuals and between nations. It can transform lives and facilitate international open honest debate, but I want to be very clear on one point in particular. When the culture of our country is used as propaganda, it diminishes arts and artists. Artists need freedom and freedom of speech to flourish. As politicians and as Governments, ours cannot be a function to stifle or to dictate art or to dictate to artists, but an artist cannot live separately from the experiences that they live in. We therefore cannot and should not always expect them to be the voice of the politics that we want to hear or be comfortable with what they have to say about government, whether they are Scottish, Israeli or Palestinian, or whether the Government in question is Palestinian, Israeli or Scottish. Cultural freedom is very precious and Governments must have the utmost respect for it. It expresses our humanity and our capacity to connect with peoples. Culture and art can and should make us challenge how we see the world. A very important part of that is to listen to another point of view, even if you disagree with it. That is very important. I think that, in listening to the different points of view that we have expressed here today, we can show that, by listening and sitting down and engaging, we can understand different perspectives, but we must always respect the rights for cultural expression and freedom of expression. That, to me, is a very precious thing indeed. In terms of the Scotland that we seek, cultural freedom should always be at the heart of how we represent ourselves to our own communities and to others internationally. Many thanks. I would like to thank all members for their elegant and dignified contributions to this important debate, and I now suspend this meeting of Parliament until 2.30.


Because it's so difficult for people to keep themselves from unconsciously touching the face, it's critical to be able to disinfect your hands by washing your hands with soap and water, sudsing up for at least 20 seconds. It's not clear why the CDC chose that duration. There is evidence that if you have bacteria-contaminated meat debris on your hands, washing with soap for 20 seconds is preferable to without soap for 5 seconds. But most of the published soap-to-soap studies compared 15 seconds to 30 seconds, and have found there does not appear to be a meaningful difference between 15 and 30. The recommendation to wash your hands with soap and water for 20 seconds was likely made to encourage sufficient hand coverage. Using invisible fluorescent or UV dyes, researchers have found the most frequently missed areas when washing your hands include the fingertips, thumbs, and backs of hands. So it's good to get into a habit of going through all the steps to cover all the surfaces instead of just happy birthing your way through the same motions. It's the time to go a little faster if you have a routine down. Oh, and artificial nails are discouraged, as they've been shown to interfere with hand-washing efficacy. Should you use hot water for hand-washing? When I gave a webinar on this topic and asked people to vote, about 1,000 out of the 5,000 participants got it wrong. Contrary to popular belief, there is no need to use hot water. Use going back more than 80 years show no benefit in germ removal when using hot water over cool water, and frequent hand-washing with hot water may increase the risk of skin irritation. And as an aside, the false belief that warm or hot water is preferable may also add an additional million metric tons of carbon through energy usage to the atmosphere from the United States alone every year. The use of hand lotions or creams has been shown to help protect hands from the minor skin damage associated with frequent hand-washing at any temperature. Now for healthcare professionals, the World Health Organization recommends the use of alcohol-based hand sanitizer, whether gel, foam, or spray over hand-washing, for routine hand disinfection. That is when hands are not visibly soiled. And so does the CDC. What type of hand hygiene is recommended? The CDC continues to recommend the use of alcohol-based hand rubs as the primary method for hand hygiene. Why? Part of the reason is greater compliance compared to hand-washing with soap and water. Just as we can't rely on people to not touch their face, we can't rely on people to wash their hands properly. In a family medicine clinic, fewer than 1 in 10 hand-washings meant even a 10-second version of the CDC standards, less than 10%. In contrast, more than 8 out of 10 instances of disinfections with alcohol-based cleansers hit the mark, which simply entails rubbing your hands together until the alcohol covers all surfaces of the hands and then waiting for the product to dry completely. Normally cheap and ubiquitous at dollar stores everywhere, hand sanitizer was one of the first items to disappear from store shelves and internet inventories as the COVID-19 crisis loomed. Anyone heating my decade-old advice on pandemic preparedness to stock up should already be well supplied, but if not, you can make your own. Although 40% alcohol, either ethanol, regular drinking alcohol, or isopropyl, found in rubbing alcohol, has been found to topically kill some envelope viruses like SARS or MERS, others like hepatitis C and Ebola virus require 60% alcohol or more as measured on a volume rather than weight basis. That's why recommended alcohol concentrations in hand sanitizers range from a minimum of 60%, recommended by the CDC, to 75% or 80% recommended by the WHO, because they want to account for a wide variety of pathogens. But what do we need specifically for COVID-19? On snopes, the social media memes at a handmade hand sanitizer made with Tito's vodka can be used to fight the new coronavirus was ruled as false, since most vodkas, including Tito's, only contain 40% alcohol, and snopes cited the CDC's 60% minimum rule. However, the CDC has since published evidence by a respected team of researchers, funded by the European Commission and German government, finding that the COVID-19 virus could be inactivated within 30 seconds by just 30% alcohol, either ethyl alcohol or isopropyl alcohol. So like 30% alcohol, 70% water wiped out the COVID-19 coronavirus. In that case, a variety of hard liquors or spirits could indeed be repurposed for use as hand sanitizers for COVID-19, either straight or even diluted to a certain extent. Vodka, rum, brandy, tequila, gin, and whiskey exceed 30% alcohol by volume. So from a COVID-19 standpoint, there are still bottles of hand sanitizer available on the shelves, just on those of liquor stores rather than drug stores. It's funny, past guests in my home are surprised to see so many big plastic bottles of cheap, 120-proof vodka in my wine rack, especially for someone who doesn't drink at all. I stocked up a decade ago following my own pandemic prep guidelines to make some extra DIY budget-friendly hand sanitizer for the next outbreak. And with the current virus, it looks like I may be even able to cut it 50-50. Note that 30% alcohol isn't enough to kill many other pathogens, so I'd still recommend 60-80% alcohol products if you can get them, so you can have one rub to rule them all. But in a pinch, during this crisis, it can be comforting to know that there may be some alternatives. Both the WHO and Interim FDA guidelines for those making their own hand sanitizer include the use of an emollient, 1.5% by volume glycerol, also known as glycerin, to help keep the alcohol from drying the skin, as well as a preservative, 0.125% by volume of the standard, over-the-counter 3% hydrogen peroxide to kill any contaminating bacterial spores. What's important for inactivating the virus, though, is the alcohol content. So here's the recipe for making a gallon. Assuming 30% alcohol is sufficient and you had all the ingredients, you can make a gallon of COVID-19 hand sanitizer by combining 12 cups of an 80-proof liquor with a quarter cup of glycerin, which is also spelled glycerin with an E or glycerol, and a teaspoon of regular-strength hydrogen peroxide, and then just fill the rest of a gallon container up with water, and nothing else. The addition of a gelling agent such as aloe vera is not recommended as it might compromise antiviral efficacy. You could also quarter the recipe to make a quart, three-cup spirits, a tablespoon glycerin, quarter teaspoon hydrogen peroxide, and water. But no need to get so fancy for this particular virus. The easiest method would probably be to just use the 80-proof liquor straight up as a hand sanitizing rub, just pour it into a squirt or spray bottle, and apply enough to completely cover all surfaces of your hands, and then rub together for 30 seconds until they're dry. On inanimate surfaces, bleach is recommended for disinfection. One part household bleach diluted in 49 parts water, so about one teaspoon bleach per cup of water, and nothing else. Never mix bleach with any other cleanser. Bleach reacts with ammonia, found in many glass cleaners, to create hazardous gases called chloramines, and reacts with acids like vinegar, or some toilet bowl and drain cleaners, and automatic dishwashing detergents, to create chlorine gas, which is also toxic. Note the more typical 1 to 100 dilution of bleach, as sometimes recommended by the manufacturer on the back of the bottle, may not be sufficient based on data from other coronaviruses. That's why it seems more appropriate to recommend a dilution of 1 to 50 of standard bleach in the coronavirus setting. Note that 1 to 50 is for standard bleach, meaning 5% sodium hypochloride. You can read the label. If you have 2.5% hypochloride bleach, you'd have to use 2 teaspoons per cup, and if you have 10% hypochloride bleach, you'd only need a half teaspoon per cup. The bleach solution can be used within a month of preparation, if stored in a closed opaque container at room temperature. Though it's recommended that you leave it on the surface you're disinfecting for at least 10 minutes, when put to the test, five minutes of that concentration was found to wipe out the COVID virus. Note that surfaces grossly contaminated by bodily secretions, meaning visibly contaminated with snot or blood or poop, may require a stronger bleach solution. One part standard bleach to nine parts water left for 10 minutes, so that would be like five teaspoons of bleach for inanimate surfaces that are visibly contaminated with bodily fluids per cup of water. Alcohol can be used on surfaces that aren't suitable for bleach such as metal, which bleach can stain or even corrode. Sufficiently concentrated povidone iodine, chlorozylonol, chlorohexidine, also have been shown to clear the virus within five minutes. Although the EPA suggests common quaternary ammonium compounds should be effective, I found an old paper that reported they were virtually useless as a sole disinfectant agent against viruses dried on surfaces, including one of the common cold human coronaviruses. Though, when put to the test, a 0.1% solution of benzalconium chloride has been found to be effective against SARS-CoV-2 within five minutes. But just a straight soap solution, one part hand soap, 49 parts water, appeared to take as long as 15 minutes to inactivate it. That would be one teaspoon liquid hand soap in a cup of water. Dishwashing detergent appears to work faster, at least against the SARS virus, with the same 1 to 50 dilution of dish soap to water working within five minutes. No word yet on dish soap in the SARS-CoV-2 coronavirus. Within 30 seconds, lysol disinfectant spray in a 1 to 64 dilution of pinesol destroy murine hepatitis virus, a mouse coronavirus that's used as a potential surrogate for human coronaviruses, since it's safer to handle in the lab than something like SARS. But lysol and pinesol have yet to be tested against the COVID-19 virus. In a pinch, wine vinegar, 6% acid, was shown to destroy more than 99.9% of SARS virus within 60 seconds, but again no word on the new virus. The most macaw decontamination advice I found was published in the Journal of the Chinese Medical Association. Corpses should be burned or buried deep.


In this video, we provide the solution to question number 12 for practice exam number one for Math 1030. In which case we have to build a minimal spanning tree for the network illustrated below using Kruskal's algorithm, which is basically just like the cheapest link algorithm. We just pick the cheapest link and avoid any cycles whatsoever. We do need to also describe what is the cost of this minimal spanning tree when we're done. Now, when I look at the network and look at the weights on the edges, the cheapest edges I see are worth 10. So I'm gonna start grabbing those. So you have like PM, which is worth 10. You have OIN, which is worth 10. You have MN, which is worth 10. Notice that I cannot use PO because that would create a cycle. Even if 20 becomes tempting later on, I can't use it. I'm gonna use MB, that's worth 10. And I'm gonna use NC, which is worth 10. A quick examination of the graph sees, I see no other vertices that are worth 10. So I think we're done there. I'm also gonna scratch out BC because that would form a premature, well, not premature.  We're looking for a spanning tree here. So I'm not gonna use BC either. So I notice I have one, two, three, four, five. Five edges that are worth 10, that gives me 50. We'll add that up, of course, later on, 50 plus. So next, let's look at some that are worth 15. That seems to be the next increment there. You have L to K, that's worth 15. You have E to F, that's worth 15. And you have I to H, which is worth 15. I'm not seeing any other 15s on the board that are acceptable. So we're gonna grab those three. So we get three times 15, that's worth 45. So next, let's look for some edges that are worth 20. All right, you have one at LM, that's worth 20. You have one at NE, that's worth 20. Now be aware, I can't use KP anymore because that would form a cycle. Can't use OF anymore because that would form a cycle, which again, those are 35, I don't really wanna use those. Those are like the most expensive ones, but nonetheless, I can't. Let's see, we did 20 and 20. Are there any other 20s on the board? I don't see any, so we're gonna add 220s onto that. That's gonna give us 40, like so. So now let's look at the board for 25. We got a 25 right here and here. I don't see any other ones. Now be aware that as we grab these, I could take one of these. Like I could take IP, but you can't take both of them because that would actually form a cycle. So I actually can only take one of them. Which one do I do? Well, Kruskal's algorithm says you're gonna choose whichever one you want. In the end, it really doesn't matter. So I'm just gonna grab PI just for the sake of example. So we're gonna get 25 in there, just 125. And so then there's a 25 right there. The next, I'm looking for some that are worth 30. Like notice vertex A right here. There's two edges that connect to it that are worth 30. I can't grab both of them because that would form a cycle. I just have to grab one of them. And it doesn't really matter which one you do. You either connect it to B or to L. I'll just go with L right there. Same thing's happening here over at D. There's two edges that are worth 30. I can't grab both of them that forms a cycle. So just choose one of them because they're just the same here. I'm gonna do DE in that situation. A similar thing is happening over here that while you are missing some edges here, like I gotta connect G to the network. I can either do it by F or H can't do both. So just for the sake of it, I'm just gonna pick F. So that's worth 30. And then likewise to connect J to the network, either go through I or K, they're both worth 30. So I'm just always picking the vertical one in this fashion right here. And so that now connects every vertex to the network. We added in four vertices, four edges, excuse me, that costs 30. That's gonna be 120 just themselves. That was the most expensive part. But anyways, when you add all these numbers together, 50 plus 45 plus 40 plus 25 plus 120, that adds up to 280. And that's the cost of this minimal spanning tree.


Ragemuffin Cat vs. Mankoon Cat. What are the differences between these two cat breeds? The Ragemuffin's breed standard describes him as a cuddly feline teddy bear. He is characterized by his large size, large walnut-shaped eyes that can be any color, sweet expression, and variety of colors and patterns. One of the interesting facts about the breed is that kittens are born white, then develop their color or pattern as they mature. Some of the differences between the Ragemuffin and the ragdoll are seen in the face. For instance, the Ragemuffin has full cheeks and the eyes are walnut-shaped rather than oval. The Ragemuffin has a broad, modified wedge-shaped head with a rounded appearance. It's supported by a short, heavy, strong neck that is especially apparent in males. Mature males are known for their jowls, giving them something of the look of a crusty old brigadier general. The broad-chested body is muscular and heavy, often with a pat of fat on the lower abdomen. A long, fully furred tail looks as if it would make a nice, soft bottle brush. Medium to medium-long fur is rabbit-soft, dense, and silky. It's slightly longer around the neck, on the sides and belly and on the hind legs. The paws and ears are furnished with tufts of fur as well. The coat comes in every color and pattern.  A Maine Coon is a big, rugged cat with a smooth, shaggy coat who looks as if they could put in a full-day mousing on a farm in all-weather conditions. Indeed, they were built for just such work in the harsh Maine climate, and their breed standard reflects their heritage, calling for a medium-sized to large cat with a well-proportioned body that is muscular and broad-chested. A Maine Coon has substantial, medium-length legs and large, round paws, well-toughed with fur, to serve as snowshoes during winter. A heavy coat is shorter on the shoulders, longer on the stomach and britches, long fur on the upper hind legs, with a rough in front and a long, furry tail waving a greeting. A medium-width head is slightly longer than it is wide and has a squarish muzzle. Large, well-toughed ears are wide at the base, tapering to a point, and large, expressive eyes are green, gold, greenish gold, or copper. White or bi-colored Maine Coons may have blue or odd eyes. The brown tabby pattern is so common in this breed that many people don't know Maine Coons can come in any other colors or patterns. They might be surprised to learn that Maine Coons are found in solid colors that include black, red or white, all tabby colors and patterns, bi-color such as blue and white or red and white, and patterns such as tortoise shell and calico. Like his cousin the ragdoll, the ragamuffin is a huggable lug who wants nothing more than to follow his people around and sit in a lap whenever possible. A nice combination of sweet and smart, he is often described as puppy-like for his friendly personality and willingness to play fetch, learn tricks and walk on a leash. He greets visitors warmly and would meet you at the door with a martini if only he had opposable thumbs. The ragamuffin is known for its docile nature. He loves to be held like a baby and will completely relax into your arms. Ragamuffins like to play but are good about limiting their attention to their toys and scratching posts, not your furniture. It is rare to non-existent for them to lay a claw on a person. This is a mellow cat but one who craves attention. Don't get a ragamuffin if you will have to leave him alone for many hours every day. The good-natured and affable Maine Coon adapts well to many lifestyles and personalities. They like being with people and have the habit of following them around, but they aren't needy. They're happy to receive attention when you direct it their way, but if you're busy, they're satisfied to just supervise your doings. Close the door on them and they will wait patiently for you to realize the error of your ways and let them in. They're not typically lapping cats, but they do like to be near you. They also retain their skill as a mouser. Even if you don't have any mice for them to chase, they'll keep their skills sharp by chasing toys and grabbing them with their big paws.  They can climb as well as any cat but usually prefer to stay on ground level. That's where their work is, after all. They're also very smart and will happily learn tricks or play with puzzle toys that challenge their brain. Maine Coons usually enjoy a kittenish level of play well into adulthood. Hello. This video is sponsored by Beemix Pets. Are you looking for high quality cat collars at an affordable cost? Check out BeemixPets.com. Use coupon code KittenLife to get 20% off. The Ragemuffin soft coat is long, but it's texture is tangle resistant. Weekly brushing or combing is all that's needed to remove dead hairs and keep them looking beautiful. The Ragemuffin has a fearless personality, so it's never a good idea to let him go outside. He has no notion that other people or animals might mean him harm and is not street smart in the least. Despite the length of the Maine Coons coat, it has a silky texture that doesn't matte easily if you groom it regularly. It is easily cared for with twice weekly combing to remove dead hair and distribute skin oils. Useful grooming tools include a stainless steel comb for removing tangles and what's called a grooming rake to pull out dead undercoat, which is what causes tangles when it's not removed. Use it gently, especially in the stomach area and on the tail. Maine Coons are patient, but they don't like having their hair pulled any more than you do. Check the tail for bits of poop stuck to the fur and clean it off with a baby wipe. They the Maine Coon is needed, which can range from every few weeks to every few months. If their coat feels greasy or their fur looks stringy, they need a bath. Brush the teeth to prevent periodontal disease. Daily dental hygiene is best, but weekly brushing is better than nothing. Trim the nails every couple of weeks. Wipe the corners of the eyes with a soft, damp cloth to remove any discharge. Use a separate area of the cloth for each eye so you don't run the risk of spreading any infection. Check the ears weekly. If they look dirty, wipe them out with a cotton ball or soft, damp cloth moistened with a 50 to 50 mixture of cider vinegar and warm water. Avoid using cotton swabs, which can damage the interior of the ear. Keep the litter box spotlessly clean. Cats are very particular about bathroom hygiene. It's a good idea to keep a ragamuffin and Maine Coon as indoor only cats to protect them from diseases spread by other cats, attacks by dogs or coyotes, and the other dangers that face cats who go outdoors, such as being hit by a car. Cats who go outdoors also run the risk of being stolen by someone who would like to have such a beautiful cat without paying for it. The common, even-tempered ragamuffin is an ideal family cat. He doesn't mind being held or carried around by a child or dressed up and pushed in a baby buggy.  Cats always teach children how to hold the cat properly, supporting both the hind end and the front end, and have little children pet him while they are sitting on the floor or on a sofa so they can be on the same level as the cat without trying to hold him. After all, he may weigh more than they do. The ragamuffin is also friendly toward other pets, including dogs, cats, birds, rodents, and lizards. To this gentle giant, everyone is his friend. Nonetheless, it's always a good idea to introduce pets slowly and in controlled circumstances to ensure that they learn to get along together. The friendly, leadback Maine Coon is a perfect choice for families with children and cat-friendly dogs. They love the attention they receive from children who treat them politely and with respect, and they don't mind playing dress up or going for a ride in a baby buggy. They're happy to live with cat-friendly dogs, too, thanks to their amiable disposition. Introduce pets slowly and in controlled circumstances to ensure that they learn to get along together. If you enjoyed this video, kindly press the like button. Also don't forget to subscribe with notifications on, so that you don't miss out on videos like this. Thank you for watching.


Welcome back to our lecture series, Math 3120, Transition to Advanced Mathematics for Students at Southern Utah University. As usual, I'll be a professor today, Dr. Andrew Missildine. In this first video for lecture 28, we can introduce the notion of modular arithmetic, which is one of the most important relations that we can place on the set of integers. Now, in previous lectures in this series, we've already introduced the notion of relations. That is how we can compare things together using Cartesian products of things. Particularly, we introduced important notions of equivalence relations and partial orders. And so as we draw to the near end of our relation unit, we introduced this important relation about modular congruence onto integers. And we'll do some more about this in lecture 29 as well. And so the congruence relation on integers is dependent upon a number, which we commonly refer to as the modulus. That modulus can be any natural number, N, ranging from zero, one, two, three, all the way up to any natural number you want there. And so with that in mind, there's gonna be different relations for different moduli. And so do pay attention to that as we go work throughout these examples here. So, okay, what is the relation then? We say that two integers, and these can be positive, negative, zero, don't care, we say that two integers, R and S, are congruence to each other, modulo N. Now, we oftentimes drop off the word modulo N if we know which modulus is in play here, but the relation does depend on the modulus. I mean, that's often abbreviated as mod short there. So we say that R is congruent to S mod N, and this will be denoted in the following way here. R is congruent to S modulo N. This happens if and only if N divides their difference R minus S, which of course, what does it mean for N to divide the difference R minus S? It means there exists some integer K such that RS is equal to K times N. So that's what this relationship here means that R is congruent to S exactly when R minus S is a multiple of the modulus N there. So let's try to take a look at some examples. So we can say that 10 is congruent to one, modulo three, because the difference between 10 and one, which is nine, is divisible by three. Nine is three times three. Likewise, we can say that 15 is congruent to zero, modulo five, because when you take the difference, 15 minus zero, which is itself 15, that's divisible by five. You get three times five there. We should see a case where it's not actually congruent. 15 is not congruent to zero, modulo seven, because like we saw before, 15 minus zero is 15, and 15 is not divisible by seven. So when it comes to these modular congruences, the modulus itself does matter very much so. So 15 is congruent to zero, mod five, but 15 is not congruent to zero, mod seven. A different modulus gives you very different things there. Just a few more examples I have here on the slide. 30 is congruent to 48, mod nine, and you can see what happens here. 30 minus 48 is equal to negative 18, and that's of course the same thing as negative two times nine here. It actually doesn't matter which order you go, because if you did it the other way around, if you took 48 minus 30, in that case you actually get a positive 18, which is equal to two times nine. And so we're gonna start, we're gonna see this in a little bit, but it turns out this relation is in fact a symmetric relation. It's also going to be reflexive. It's also gonna be transitive. Oh, that kind of sounds like an equivalence relation, right? We'll see that in just a little bit before the end of this video. But one more example here, 23 is congruent to two, mod seven, because 23 minus two is equal to 21, and 21 is divisible by seven, okay? So this gives us this notion of the congruence modulo sum natural number here. And just so you're aware, when we talk about the natural numbers here, this includes zero as an option. You can ask, like, are integers congruent modulo zero? A lot of authors, when they talk about modular integers, they don't allow for zero. They only allow for positive integers in that case. But there's actually nothing wrong with doing zero, mod zero here. It's kind of interesting because in that situation, if you have A is congruent to B mod zero, what that means is zero divides A minus B, all right? And so we need some integer K such that K times zero, which has to be zero is equal to A minus B here. You get A minus B. And so it's kind of silly here, but if two integers are congruent mod zero, they actually have to be equal as integers. So modulo zero doesn't give you a new relation. It's just the usual equality relation on integers. But as you take other moduli, you can get a different relation. And so it's not wrong to include zero. A lot of people omit it because it's not offered anything new. But I do want to point out that modulo zero does make sense. Now, people often include the positive integers there. And I'd like to mention that if you ask our things congruent modulo one, it's honestly just as silly to talk about modulo one as it is modulo zero, because if A is congruent to B modulo one, that means that one divides A minus B. But hey, one divides everything, right? One divides every integer. So we need to have A minus B, which is equal to K times one, but the K is just A minus B itself times one. So that's sort of the other extreme. When you're mod zero, you just get the usual equality here. But if you're mod one, you get that everything is congruent to each other. So we don't usually work mod zero, mod one, because there's kind of these silly trivial cases. But when you start talking mod two, mod three, mod four, this gives you a very interesting relation on the integers. And I should also mention that if you're trying to tech this thing up, this symbol right here is backslash equiv short for equivalent. And then also this symbol right here, you're actually gonna do, there is a backslash mod command, but it doesn't get the spacing right all the time. You wanna use backslash pmod, for which it then takes in your modulus as a command. That'll put the spacing and the parentheses just right. They'll make it look adorable in your latex documents there. So with a relation now in hand, it makes sense to consider properties about that relation. I hinted to the fact that it's an equivalence relation. We will get to that in just a moment. I actually wanna look at some algebraic properties that this congruence modulo n satisfies, which is actually one of the reasons why we care about it so much. So imagine we have three integers abc, and we have a modulus n, then it does hold that if a is congruent to b modulo n, then a plus c will be congruent to b plus c modulo n. So the idea here is that if you have two numbers that are congruent to each other, if you add the same value to both sides, you still be congruent to each other. So in some aspects, like this is what equality does, right? If a equals b is integers, then a plus c equals b plus c. So this congruence modulo n will satisfy this variance under addition property, okay? And to see that, let's just go through the proof. Let's look at the definitions of these things. Suppose that a is congruent to b modulo n. Well, that means there exists, so of course this means that n divides a minus b. So there exists some integer k such that ab is equal to kn. I want you to now to consider the difference of a plus c minus b plus c, because what we wanna do is we wanna show with this one over here, if a plus b is congruent, excuse me, if a plus c is congruent to b plus c, that means that a plus c minus b plus c is supposed to be divisible by n. That's the definition there. So we're gonna consider the difference there, a plus c minus b plus c, but notice the c's cancel out, you just get back a minus b again, which of course as we observed earlier was k times n. So n does divide the difference of a plus c and b plus c. So this tells us that a plus c is congruent to b plus c. So if you have two integers that are congruent, then adding the same number to both sides will still make it congruent, all right? A similar property here. If you have three integers, a, b, c, and you're working modulo n, if a is congruent to b modulo n, then a minus c is congruent to b minus c mod n. Now, this is one of those situations where I'm gonna leave the proof up to the reader, or proof up to the viewer in this regard here. This is something that's commonly done in mathematical courses and textbooks, and that's because the proof here is so similar to the previous one that me providing a second one is not gonna do you any good, but you writing it actually will be very educational for you. And honestly, it's just take the previous proof that's now off the screen and change the appropriate parts. You're gonna get subtraction as well. So integer congruence, it's invariant under addition. It's also invariant under subtraction. You perhaps can see where we're going here. What about integer congruence? Is it invariant under multiplication? If I take three integers, a, b, c, and a modulus n, if a, b is congruent to, sorry, if a is congruent to b mod n, then a, c is congruent to b, c mod n, all right? So I claim that integer congruence is invariant under multiplication, all right? We're doing the exact same type of proof that we did before. Again, you just unravel the definition of this relation. So suppose that a is congruent to b modulo n, that means there's some integer k such that the difference a minus b is equal to k times n. So now I wanna show this congruence is gonna hold. So I have to consider the difference a, c minus b, b, c here. I need to argue that n divides this difference. So I'm gonna consider the difference there, a, c minus b, c. But this is just an algebraic statement of integers. a, c minus b, c, there's a common divisor of c that you can factor out, c times a, b. And by assumption here, a minus b is equal to k, n. So we get that a, c minus b, c is equal to c times k, n. Therefore, n divides a, c minus b, c. And that then gives us that a, c is congruent to b, c. So all right, so what we have so far is that integer congruence is invariant under addition, subtraction, and multiplication. What about division? Division gets a little bit more problematic because, well, if you divide two integers, you don't necessarily get an integer anymore. Like one divided by two is not an integer. And so division is a little bit more problematic. We will consider that in our next video there in our lecture series. So going on, I do want to mention another property here. If we have two integers a and b, and we have a modulus n, if a is congruent to b mod n, it's also true that the squares are congruent to each other as well. a squared is congruent to b squared mod n. And the proof is basically the same. Suppose a is congruent to b mod n. Then there exists some integer k such that a, b is equal to kn. If I want to show that a squared is congruent to b squared, I need to consider their difference, a squared minus b squared. I need to argue that n divides a squared minus b squared. So we take that difference right there, a squared minus b squared. Now, that isn't difference of squares. I can factor that thing.  And while I don't know anything about a plus b, I do know that a minus b is divisible by n. So we can make that substitution here. a minus b is equal to kn. Therefore, a squared minus b squared is equal to a plus b, which is something, times kn. We then can see that n divides the difference of squares. n divides a squared minus b squared. And this then gives us that a squared is congruent to b squared mod n. And I want to mention that this actually continues on for other powers as well. While the factorization is a little bit more complicated, you can do a similar argument that a cubed is congruent to b cubed. a to the fourth is congruent to b to the fourth. a to the 5 is congruent to b to the 5, et cetera, et cetera. So in general, we can actually replace this with the following a to the n. We already have an n. a to the m is congruent to b to the m modulo n. That all exponents are going to be congruent to each other if a to the b is, if a is congruent to b here as well. So we've looked at all these algebraic properties of modular arithmetic. And this is actually why we refer to it as modular arithmetic. We can actually get some very nice arithmetic properties. Again, we'll delve into that a little bit more into the next video here. So before we end this video, there is one more thing I do need to talk about. So let's play with this definition a little bit longer here. So note, if a is congruent to b mod n, this implies that n divides the difference a minus b. Now I want us to do some division here. We talked about division a little bit earlier. While we're not gonna do modular division in this video, think about the division algorithm on integers.  Then we can do the same thing here. If I take b and divide it by n, there's gonna exist some quotient and remainder called them p and s such that b is equal to pn plus s where again, we can assume that s is congruent equal to zero, but less than n. Like so, again, this is a consequence of the division algorithm, all right? So if you take this divisibility statement, n divides a minus b, clearly you can also observe that n divides q minus p times n. I mean, clearly you can see the factorizations there. Why is that relevant? Well, then I claim that n divides the difference of the remainders, r minus s like so. And so notice that r, based upon the original equation if you solve for r right here, r is the same thing as a minus qn. And similar, if you solve this equation for s, you're gonna get that s equals b minus pn.  Simplifying those things, you're gonna get an a minus b minus a q minus p times n here.  And therefore it has to be the case that n divides r minus s because r minus s is a difference of things divisible by n. But this is where this comes into play now. Remember, r is less than n, so is s. So when we take the difference of r minus s, since r is less than n, this difference has to still be less than n. But since s itself also is less than n, when we take this difference here, I'm not supposing r is the bigger of the two, but the point is this difference has to sit somewhere between, has to sit somewhere in between n and negative n. But n divides this. And so the only possibility, the only multiple of n that sits in between n and negative n is gonna be zero. So we can actually conclude that r minus s is equal to zero, which then tells us that r equals s. And so now summarizing what we just discovered here, if a is congruent to b mod n, it actually means that a and b have the same remainder if divided by n. And when you use that word same remainder, they have the same remainder when you divide by n. This is then to suggest why this is in fact an equivalence relation. An equivalence relation measures when two things are somehow the same. And this congruence modulo n relation is measuring what is the remainder. When things have the same remainder, they're gonna be congruent to each other. This is in fact an if and only if statement. We went in one direction. We show that if they're congruent, they'll have the same remainder, but you can actually go the other way around. If they have the same remainder, then they'll be congruent modulo n. And you can reverse the directions. I'll leave that as an exercise to the viewer here. So in particular, this congruence relation is an equivalence relation. Let's prove it officially here. Congruence modulo n is an equivalence relation on the integers for any positive integer n. And honestly, I can just say any natural number. Any natural number. It doesn't have to be just to be a positive. It could be zero as well. So let's first argue that it's reflexive. So note that if I take r minus r, that's equal to zero. And zero is gonna be equal to zero times n. So regardless of what your modulus is, we do get that r is congruent to r. So this is a reflexive relation. Symmetry, we've talked about that a little bit already, but let's prove it now. If r is congruent to s modulo n, that means that r minus s is equal to kn for some integer here.  On the right-hand side, you're gonna get negative k times n. This shows that n divides s minus r because negative k is still an integer. This then shows that s is congruent to r mod n. So if r is congruent to s, then s is congruent to r. We have the symmetric property. Now, the last one to be an equivalence relation is we have to do transitivity. This one's a little bit longer, but we can handle it. So for transitivity, we have to show that if r is congruent to s and s is congruent to t, we then wanna show that r is congruent to t. That's what our goal is. So, okay, so assume r is congruent to s and s is congruent to t. Now, if r is congruent to s, that means that n divides r minus s. So there's some integer k such that r minus s is equal to k. Likewise, if s is congruent to t, then that means that s minus t is divisible like n. So there exists some integer, we'll call it l, such that s minus t is equal to l times n. So then what we're gonna do is we're gonna take these two expressions and combine them together. Cause notice, if I take r minus t, this is the same thing as r minus s plus s minus t. The s is canceled out in this situation. But of course, the advantage here is r minus s is the same thing as kn, s minus t is the same thing as lk, sorry, ln. And so kn plus ln, you can factor that as k plus ln, which of course, k plus l is an integer. And so this shows us that r minus t is divisible by n and that then gives us that r is congruent to t mod n. So we do in fact have an equivalence relation for any natural number. And this proof never required anything other than we had a natural number there. So we can extend this, even though we're never gonna work mod zero or mod one, be aware this proof holds for every possibility, every possible natural number there. So because we have an equivalence relation, it makes sense that we can talk about the equivalence classes. Every equivalence relation provides a partition on the set associated to the equivalence relation. And that gives us our equivalent classes. So since this is an equivalence relation, what would the equivalence classes be when we work mod n? For this example, we're gonna do specifically n equals three. So it turns out that if you're doing integer modulo, integers modulo three, you're gonna get three equivalence classes. Just so you're aware in the situation of modular arithmetic, these are commonly referred to as the congruence classes. So the congruence classes are just the equivalence classes associated to the equivalence relation congruence modulo n. Now, if you're working mod three, you're gonna get three congruence classes. There's gonna be the class that is represented by zero. This will include zero, three, six, nine, 12, 15, negative three, negative six, negative nine, et cetera, and particularly it's gonna get all of the multiples of three. Because remember, these elements are equivalent to each other, the congruent to each other, if they have the same remainder when you divide by three. And so the multiples of three are gonna be those numbers. When you divide by three, you get a remainder of zero because they're actually multiples of three. Likewise, there is going to be a congruence class associated to the number one. This will include one, four, seven, 10, 13, negative two, negative five, et cetera. These numbers are those numbers for when you divide by three, you get a remainder of one. Another way to think about it here is that when you go from the next one to the next one, you're just adding three. One plus three is four, plus three is seven, plus three is 10, plus three is 13. This sequence forms an arithmetic progression where you're increasing three each and every time. That was also true, of course, for the multiples of three. And then the last congruence class here is gonna be the congruence class represented by two. This will include two, five, eight, 11, 14. Notice you can get from one number to the next just by adding three over and over again. If you subtract three, you go the other way around, negative one, negative four, et cetera. Again, this set forms an arithmetic progression where you're increasing throughout the sequence always by adding three there. And so these are the three congruence classes associated to the integers mod three. If you take the union of each of these things, so the union of the congruence class for zero, one, and two gives you all of the integers. These sets are in fact disjointed, forms a partition. And there's just the three of them, just the three of them. The set, these three congruence classes gives you all of them. And it's not a coincidence that there are three congruence classes, and our modulus was three as well. Okay? So again, excluding the case where your modulus is zero or one, that's where you can get a little bit weird here. I guess one's not so weird in this situation, but in general, what you see is if you take any modulus whatsoever, n, the number of congruence classes that you have is gonna equal n. So working modulo n, you get n, congruence classes. And each of these classes can be represented of the form, the congruence class of x, where x is some number that sits between zero and n. Because after all, the congruence classes are determined by the remainder of the integer we divide by n. And by the division algorithm, the remainder will sit anywhere between zero and n, not including n, but you can get zero. So you get zero, one, two, three, four, five, all the way up to n minus one. So your congruence classes look exactly like that. You get a congruence class for zero, congruence class for one, congruence class for two, all the way up to a congruence class for n minus one. All of the possible remainders when you divide by n, you get those. And so these remainders are actually like the poster child for the congruence classes. It's the ideal representative for that. We can always denote the congruence class using the remainders, because they all have that common remainder. All right? Like I said, zero is a little bit funky in that situation, because in that case you have, it's a little bit different. But for any pause, integer, this statement would then in fact hold. So what we're gonna do as we end this video is we're gonna introduce a new symbol. We're gonna denote the symbol z sub n to be the set of congruence classes. All right, so z sub n as a set will contain the congruence class zero, the congruence class one, the congruence class two, all the way up to the congruence class of n minus one. Like so. I should then note that the cardinality of this set is in fact equal to n. Again, so long as n doesn't equal zero. Zero is a little bit exceptional in this case. It doesn't, the definition of the relation makes sense when it equals zero, but this set n sub zero is a little bit weird if you have zero in there. So we'll only do that for positive integers. This is the main reason why zero gets kicked out. But we then define this set n sub zero to be the set of all congruence classes on the integers module n. And I want to mention that this is sort of an analog to how we define the rational numbers. Remember the rational numbers, we then define to be a set of congruence classes. We write p over q, where of course p and q are integers, where q doesn't equal zero. But that number, the number p over q is really just a congruence class for these ordered pairs that we had talked about previously when we introduced congruence classes or when we introduced equivalence equations, I should say. So the rational numbers by definition is a set of equivalence classes. We're gonna do the same thing with these modular integers. And we're gonna see next time, just like how q has a very nice algebraic structure that we can add to track both by divide. We can do a similar thing for z sub n, but again, we'll do that one next time.