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 $x \notin (A \cap B)$?

It's true that $x \in A \land x \not\in B \implies x \not\in A \cap B$, but its converse is false: if $x \not\in A \cap B$, it's possible that $x \notin A \land x \notin B$, and this renders $x \in A \land x \not\in B$ false.
