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Let A = {n ∈ Z | n = 5r for some integer r} and B = {m ∈ Z | m = 20s for some integer s}. a. Is A ⊆ B? Explain. b. Is B ⊆ A? Explain

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Let A = \{n\in\mathbb Z\ |\ n = 5r\ \text{for some integer}\ r\} and B = \{m\in\mathbb Z\ |\ m = 20s\ \text{for some integer}\ s\}.


a. Since n=5=5\cdot1 and 1\in\mathbb Z, we conclude that n=5\in A. On the other hand, n=5\ne20\cdot s for each integer s, and therefore, n=5\notin B. We conclude that it is not true that A\subseteq B.


b. If m\in B then m = 20s for some integer s. It follows that m=5(4s), 4s\in\mathbb Z, and consequently, m\in A. Therefore, B\subseteq A.

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Question ID: mtid-5-stid-8-sqid-3554-qpid-2253