Thayer Watkins
Silicon Valley
& Tornado Alley

Relations and Relation Algebra

Relation is a mathematical concept as well as a common-life concept. A relation such as is a sibling of is familiar. Given any two individuals one can usually say whether the relation holds or not. While is a sibling of is symmetrical other relations such as is a sister of are not. Relations may or may not be reflexive. The relation is not older than is reflexive because it is true of one person in comparison to his or her self, but is older than is not reflexive because it does not apply to a person with respect to her or himself.

Some relations are transitive. For example, is older than is transitive because if x is older than y and y is older than z then necessarily x is older than z. Other relations are not transitive. Consider is an enemy of. If x is an enemy of y and y is an enemy of z then x might well not be an enemy of z.

(To be continued.)

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