Brackets are used specify the order of evaluation, just as in
maths. 5 * 2 + 3 is 13 because multiplication takes precedence
over addition, but if you wanted the addition first you'd write
5 * (2 + 3) which is 25.  It's the same with Boolean algebra.
NOT A AND NOT B is the same as (NOT A) AND (NOT B), because NOT
takes precedence, so NOT (A AND NOT B) just means that you want
the inverse of A AND (NOT B).  To show that the two expressions
are not equivalent basically this means that you must draw out
the truth table for both. I find it easier to build it up with
multiple columns rather than to try and work it all out for each
line, so if the first column is A, the second B, the third NOT
A, the fourth NOT B and the fifth the AND of the third and
fourth, i.e. (NOT A) AND (NOT B), we get the following: A B !A
!B (!A . !B) 0 0  1  1  1  0 1  1  0  0 1 0  0  1  0 1 1  0  0
0 So do the same for NOT (A AND NOT B). Make the first two
columns A and B, the third NOT B (just invert the second), the
fourth A AND NOT B