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Is this the correct contrapositive?

  1. Apr 3, 2010 #1
    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.
  2. jcsd
  3. Apr 4, 2010 #2


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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:
  4. Apr 4, 2010 #3
    Thank you so much for your response and the welcome. Greatly appreciated.
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