Theorem: If n^2 is positive, then n is positive.
Proof: Suppose that n^2 is positive. Because the implication is true, we can conclude that n is positive.
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What is wrong with the following argument (which purports to show that n is an even integer whenever n^2 is an even integer): Suppose that n^2 is even. Then n^2=2k for some integer k. Let n=2m for some integer m. This shows that n is even.
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Proof: Suppose that n^2 is positive. Because the implication is true, we can conclude that n is positive.
________________________________________________________________________________
What is wrong with the following argument (which purports to show that n is an even integer whenever n^2 is an even integer): Suppose that n^2 is even. Then n^2=2k for some integer k. Let n=2m for some integer m. This shows that n is even.
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