Is this the correct contrapositive?

  • #1

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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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:
 
  • #3
Thank you so much for your response and the welcome. Greatly appreciated.
 

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