Question: Test the following binary relations on the given sets S for reflexivity, symmetry, antisymmetry, and transitivity. Explain your answer.
a. S = Q (set of rational numbers), x ? y ? |x| <= |y|
b. S = Z (set of integers), x ? y ? x – y is an integral multiple of 3
c. S = N (set of natural numbers), x ? y ? x . y is even
d. S = N (set of natural numbers), x ? y ? x is odd
e. S = set of all squares in the plan, S1 ? S2 ? length side of S1 = length side of S2