Thank you both for your help. However, I am getting more confused.

First Defunkt, I thought I was doing what you said needed to be done by showing arbitrary elements of both

and

were in the union to prove reflexive. So I don't see how exactly I was working backwards. I know my proofs are not "up to par" and I saw my professor yesterday to get help. I am trying to learn and not trying to be argumentative. Should I maybe have said

and

were arbitrary? Thank you for your patience and understanding.

Plato, again thank you for your help.

I don't see how transitivity does not work for the union. (1,2) (2,1) (2,3) (3,2) are all in the union.

What if

={

} and

={

} with their intersection equal the null set. Would that be an equivalence relation?