= Solution
Let two distinct quotient points correspond to two <equivalence classes>. By <hypothesis> those classes lie in disjoint <open> saturated sets $U,V\subseteq X$. Saturation gives $p^{-1}(p(U))=U$, so the quotient definition makes $p(U)$ <open>, and likewise $p(V)$.
The image sets contain the two quotient points and are disjoint. Indeed, a class meeting both $U$ and $V$ would be contained in each because both sets are saturated, contradicting their disjointness. Thus \b[the quotient is <Hausdorff>].
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