= Solution
{c}
The <Mostowski collapse theorem> applies when $E$ is a <well-founded relation> and an <extensional relation> on the set $M$. Extensionality here means that different points have different sets of $E$-predecessors. There is then a unique <transitive set> $T$ and a unique <bijection> $\pi:M\to T$ such that
$$
\boxed{x\,E\,y\iff\pi(x)\in\pi(y).}
$$
The collapsing map is characterized by <well-founded relation> recursion:
$$
\pi(x)=\{\pi(y):y\in M,\ y\,E\,x\}.
$$
Thus $(M,E)$ is isomorphic to $(T,\in)$. Both well-foundedness and extensionality are hypotheses of the theorem; well-foundedness alone does not make the recursive map injective.
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