## Related questions with answers

Question

A student wrote the following conjecture. Find a counterexample and explain the error. If x is a positive even number and y is any integer, then the product xy will be positive.

Solution

VerifiedStep 1

1 of 2A possible counterexample is when $y$ is 0 or any negative integer, say $y=-2$. Since $x$ is positive, then then product $xy$ will be negative in this case.

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