Prove set intersection is null The questions asked me to prove this. 
I have no idea what I'm doing and I do not have the book. Prove If $A$ is a subset of $B$, and $B\cap C=\emptyset$, then $A\cap C=\emptyset$.

Assume that $
A\cap C\neq \emptyset
$. Then there is $x\in A$, suc as $x\in C$. As $A\subset B$, $x\in B $ (and $x\in C$). So $B\cap C\neq \emptyset$.
