Is this the correct contrapositive?

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SUMMARY

The discussion centers on the concept of contrapositives in logic, specifically regarding integer products. The first statement, "If x and y are two integers whose product is even, then at least one of the two must be even," has the correct contrapositive: "If both x and y are odd, then the product of x and y is odd." Additionally, the second statement, "If x and y are two integers whose product is odd, then both must be odd," correctly leads to the contrapositive: "If either x or y is even, then the product of x and y is even." The participants confirm the understanding of negating quantifiers and the transformation of logical statements.

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someperson05
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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.
 
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Welcome to PF!

Hello someperson05! Welcome to PF! :wink:

Yes, that's all fine …

you've grasped the general principle that the contrapositive of P => Q is notQ => notP, and "and" becomes "or" etc. :smile:
 
Thank you so much for your response and the welcome. Greatly appreciated.
 

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