Let Z denote the set of integers. Which of the following relations E are equivalence relations? Explain.

(a) xEy (if and only if) x – y is an even integer

(b) xEy (if and only if) x – y is an odd integer

*I seem to have a lot of trouble on these relation type problems. Thank you to everybody who has helped me with these problems.

The thing that stands out at is that the only difference above is one is even and one is odd. Also, I know I will have to use Reflexivity, Symmetry, Transitivity to solve the problem.