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Question

# Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The product of a positive integer and a negative integer is never a positive integer. ____

Solution

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We need to determine whether the product of a positive integer and a negative integer could ever be some positive integer.

Let $x$ be a positive integer and $-y$ be a negative integer. Note that this implies that $y$ is a positive integer.

$x\cdot (-y)=-(x\cdot y)$

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