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## Main Question or Discussion Point

Hello, I have a real simple question.

Given, If x and y are two integers whose product is even, then at least one of the two must be even.

Is the contrapositive, If both x and y are odd, then the product of x and y is odd?

Similarly, If x and y are two integers whose product is odd, then both must be odd.

Is the contrapositive, If either x or y is even, then x and y are two integers whose product is even?

For some reason I get confused when it becomes an issue of negating quantifiers.

Thank you for your help.

Given, If x and y are two integers whose product is even, then at least one of the two must be even.

Is the contrapositive, If both x and y are odd, then the product of x and y is odd?

Similarly, If x and y are two integers whose product is odd, then both must be odd.

Is the contrapositive, If either x or y is even, then x and y are two integers whose product is even?

For some reason I get confused when it becomes an issue of negating quantifiers.

Thank you for your help.