Products Are Odd Iff Factors Are Odd

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Problem 42: (Products Are Odd Iff Factors Are Odd)

Let $x$ and $y$ be integers. Consider the implication below.

• If $xy$ is odd, then both $x$ and $y$ are odd.

Write the contrapositive of this implication. Then write the negation of this implication. Then prove that the implication is true by either proving the contrapositive to be true, or by proving that the negation is false.

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