What are the pairs in a relation R on set A?

Question

Consider the set A = {0, 1, 2, 3, 4, 5, 6}. The relation $ xRy \iff 2 | (x - y) $. What is relation R?

My answer is R = {(2,0), (4,0), (6,0), (3,1), (5,1), (4,2), (6,2), (6,3), (0,2), (0,4), (0,6), (1,3), (1,5), (2,4), (2,6), (3,5)}.

2 Questions:

1. Is that correct?
2. What about pairs like (x, x) like {(0,0), (1,1), ... , (5,5), (6,6) }

Sorry if this is like a simple question but I have just started on relations...and the solutions sheet that I was given wasn't filled.

Any comments/answers is very much appreciated! Thanks in advance!

Answer 1

R = { (x,y) : x and y are both even or x and y are both odd }
Exercise. Prove R is an equivalence relation.