The question states:
Determine whether each of the binary relations R defined on the given sets A is reflexive, symmetric, antisymmetric, or transitive. If a relation has a certain property prove that is so; otherwise, provide a counterexample to show that it does not.
i) A = N; (a, b) belongs to R if and only if a does not equal b
ii) A = Z; R = {(x,y) | x + y = 10}.
I do not not know where to start with either of these because I am not sure how to compare the sets. Could someone please start me off in the right direction. Thanks.