Solution
= Solution
The relation is <reflexive> because $a-a=2\cdot0$. It is <symmetric> because $a-b=2k$ implies $b-a=2(-k)$. It is <transitive> because $a-b=2k$ and $b-c=2\ell$ imply $a-c=2(k+\ell)$. It is therefore an <equivalence relation>, namely <congruence modulo an integer> for modulus two. Its two <equivalence classes> consist of the <even integers> and the <odd integers>.