I've got another question.
Let R be a relation on A. (a,b) 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 A such that a Z.
if 3a + a = 4n
then a = n and (a,a) R.
I assumed that because we have IFF I have to go the other way...
if (a,a) 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?