1. Determine if the set is CLOSED or NOT CLOSED. Let + and \cdot be usual binary operations of addition and multiplication of \(\mathbb{Z}\) and let \(H = \{n^2 | n \in \mathbb{Z}^+\}\). Is H closed under addition? Under multiplication?
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Let's take two arbitrary elements from H, say a and b. Since a and b are both positive integers, their sum, a + b, will also be a positive integer. Show more…
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