Equivalence relation on class of all sets Let $\mathcal{A}$ be the class of all sets. Prove that "has the same cardinality as" defines an equivalence relation on $\mathcal{A}$.
I know that equivalence relations must be reflexive, symmetric and transitive. So I think the best way to go about this would be to just show that each individual property is satisfied.... but I think I need to do more than just say hey look, this is obvious. And I am not even sure where to start.

Yes, you should just show that each individual property is satisfied
Reflexivity: The identity function works ($1_A: A \to A$). 
Symmetry: Given $f: A \to B$ bijective, consider $f^{-1}:B \to A$.
Transitivity: Given $f: A \to B$ and $g:B \to C$, what can you say about the composition $g \circ f: A \to C$?
