Let A and B be sets and let f: A --> B be a function.

Define a relation on A as follows. If a,b in A, we say that aRb if and only if there exists some c in B such that f(a) = c and f(b) = c. Prove that R is and equivalence relation on A.

Ok, I know that i need to show the 3 properties. transitive, symmetry, and reflexsive. I also notice that f(a)=f(b). can i assume that a=b?

thanks