Let $W$ be a binary relation on a set $Y$. The relation $W$ is called extensional if $$ \forall x,y \in Y (x \neq y \rightarrow \exists z \in Y (( \langle z,x \rangle \in W \land \langle z,y \rangle \notin W) \lor ( \langle z,x \rangle \notin W \land \langle z,y \rangle \in W )))$$
Consider the $\in$ relation. Let $Y$ be a set that is not transitive. This means that there is $y$ in $Y$ such that $x \in y$ but $x \notin Y$. (Right?) How does this make $\in$ non-extensional?
(As I understand extionsionality means that two sets are equal if and only if they contain the same elements. How is this violated if $\in$ is not transitive?)
Here is a copy of the exercise, page 64, Just/Weese: