True or False: $A\cap (B\times C)=(A\cap B)\times (A\cap C)$ True or false. Prove by showing the statement is true in general or by giving a counter example.
$A\cap (B\times C)=(A\cap B)\times (A\cap C)$
I'm not sure what the question is trying to get at. Maybe there is some way to write the left to look like the right?

Take $A=\{0, 1\}, B=\{1,2\}, C=\{0,1\}$. Therefore, $A\cap (B\times C)=\{0,1\}\cap\{(1,0), (1,1), (2,0), (2,1)\}=\emptyset$, but $(A\cap B)\times (A\cap C)=\{1\}\times\{0,1\}=\{(1,0), (1,1)\}$, and therefore, this isn't true.
