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Given a countable set ${A}$ and an infinite set ${B}$, prove or disprove that ${A}\setminus{B}$ is finite. By the way a countable set can never be a subset of an infinite set, is that true?

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A countable set is always a subset of an infinite set. –  Brian M. Scott Apr 11 '12 at 8:47

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up vote 3 down vote accepted

The statement is false. For example, let $A=\mathbb N$, the set of natural numbers, and $B=\{2n : n\in \mathbb N\}$, the set of even natural numbers. This also answers your second question (the answer being "no, it is false"), as $B$ is countable and is a subset of $A$ which is infinite.

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