= Solution
\b[True.] For nonempty <connected spaces> $X,Y$, choose $x_0\in X$, $y_0\in Y$. For each $x\in X$, the subspace $(X\times\{y_0\})\cup(\{x\}\times Y)$ is <connected>: its two <connected> pieces meet at $(x,y_0)$. The union of these subspaces over $x$ is all of $X\times Y$, and every piece contains the common <connected subset> $X\times\{y_0\}$. Their union is therefore <connected>. The assertion is also true if a factor is empty, since the empty product space is <connected>. This proves <product of connected spaces>.
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