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Consider the following definition: An integer n is sane if 3(n2+2n) a. Give a counterexample to the following statement: All odd integers are sane. b.

image text in transcribed Consider the following definition: An integer n is sane if 3(n2+2n) a. Give a counterexample to the following statement: All odd integers are sane. b. Give a direct proof of the following statement: If 3n, then n is sane. c. Prove by contradiction: If n=3j+2 for some integer j, then n is not sane

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