Hey guys! I'm brand new to set theory; I just started learning it as a hobby. I just finished the section on cartesian products, and I'm a bit hung up on one of the exercises.

Let A,B,X, and Y be sets. A contains X, and B contains Y.

Prove that C(XxY) = AxC(Y) U C(X)xB

Mendelson's Intro to Topology was a bit vague on what the complement of a cartesian product would be (and by a bit vague, I mean completely silent). I'm guessing that C(XxY) would = {(q_{1},w_{1)},(q_{2},w_{2}),...(q_{n},w_{n})} where q is not in X and w is not in Y, yes?