Does $x \in A$ and $x \notin B$ imply that $x \notin (A \cap B)$? For any two sets $A$ and $B$. Is it true that if $x \in A$ and $x \notin B$, then $x \notin (A \cap B)$?

Two logical statements defining two sets in set theory are only equivalent if and only if the sets they define are equal. In the current question this is not so: $x\notin A\cap B$ even if $x\notin A$ and $x\in B$.
