= Solution
\b[False.] The <rational numbers> $\mathbb Q$ with their <subspace topology> from $\mathbb R$ are Hausdorff. If a subset contains two distinct rationals $a<b$, choose an irrational $c$ between them; intersecting the subset with $(-\infty,c)$ and $(c,\infty)$ gives a separation into two nonempty relatively open sets. Thus every nonempty <connected subset> of $\mathbb Q$ is a singleton, so it is <totally disconnected>. Yet no rational is isolated, because every interval around it contains another rational. Therefore $\mathbb Q$ is not a <discrete space>. Hausdorffness and total disconnectedness do not imply discreteness.
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