a) Show that a subset of a countable set is countable.

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Let $B$ be a subset of a countable set $A$ . By defenition of a countable subset, there is an injection $f:A\to \mathbb N$ . Since the restriction $f|_B:B\to\mathbb N$ of an injection $f$ to the subset $B$ is an injection as well, we conclude that $B$ is a countable set.

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Question ID: mtid-5-stid-8-sqid-3471-qpid-2170