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N a) ∪ Aj j=1 Each Aj is the set { j}, so every Aj fully contains the sets Aj1 Aj2 etc as subsets Therefore, the union of the sets A1 through An is exactly An We can take this one step further and say that, since n is unbounded, An, in fact, is the set (∞,∞) n b) ∩ Aj j=1. ƒ(1) = 1, and ƒ(2) = 1 12) (8 points) Give an example of a function from N to N that is (There can be many possible answers to. B) ƒ(n) = n2 1 No This can proved by a counter example;.
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ƒ(1) = 2, and also ƒ(1) =2 c) ƒ(n) = n3 Yes Because this is a strictly increasing function d) ƒ(n) = n/2 No This can be shown by a counter example;.

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