I was in class the other day when I got a problem presented to me to that I had to figure out.
The problem was "If A X B is a subset of C X D, then A is a subset of C and B is a subset of D. Prove this is true or give a counterexample to show it is false."
If $A\times B \subseteq C \times D$, then $A\subseteq C$ and $B\subseteq D$. Prove this is true or give a counterexample to show it is false.
I'm almost positive that this is false but I'm not sure how to go about disproving it.
If anyone could help me out at all I'd appreciate it.
Thanks a lot.