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**Alterah** I've got another question.

Problem:

Let R be a relation on A. (a,b) $\displaystyle \in$ R IFF 3a + b = 4n for some integer n. Prove that R is an equivalence relation on Z.

I assumed the Z part was a typo, but am not sure now...

I know I need to show that R is reflexive, symmetric, and transitive.

For Reflexive I've got:

Let a $\displaystyle \in$ A such that a $\displaystyle \in$ Z.

if 3a + a = 4n

then a = n and (a,a) $\displaystyle \in$ R.

I assumed that because we have IFF I have to go the other way...

if (a,a) $\displaystyle \in$ R, then 4a = 4n and a = n which checks.

For Symmetric and Transitive...I am at a loss, don't I have to do two statements here for the IFF...or am I getting confused and using given information in the proof?