3. Consider the relation 5 on Z dened as follows: x 5 y if and only if...

3. Consider the relation ≡5 on Z defined as follows: x ≡5 y if and only if 5 | (x−y). In this problem, you’ll be proving that ≡5 is an equivalence relation. That means that you’ll need to prove that it is reflexive, symmetric, and transitive.

(a) Prove that ≡5 is reflexive. Again, this will be a relatively short proof, but not quite a one-liner.

(b) Prove that ≡5 is symmetric. (Yes, you already did this problem on one of the mini-homework assignments. You don’t have to redo the problem, but you should at least copy over your answer from that assignments to this one.)

(c) Prove that ≡5 is transitive.