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Arrange the steps in the correct order to prove the theorem "If A and B are sets, A is uncountable, and A ⊆ B, then B is uncountable."

Arrange the steps in the correct order to prove the theorem "If $A$ and $B$ are sets, A is uncountable, and $A \subseteq B$, then $\mathrm{B}$ is uncountable." Rank the options below. Since $A$ is a subset of $B$, taking the subsequence of $\left(b_{n}\right)$ that contains the terms that are in $\mathrm{A}$ gives a listing of the elements of $\mathrm{A}$. Thus $B$ is not countable. Assume that $B$ is countable. The elements of $\mathrm{B}$ can be listed as $b_{1}, b_{2}, b_{3}, \ldots$ Therefore A is countable, contradicting the hypothesis.

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