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Math Help - can you use parity tables as proof?

  1. #1
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    Question can you use parity tables as proof?

    can you use parity tables as proof?

    I want to use it to prove this:

    if mn is even, then at least one of m or n is even.

    (very basic but can I use it as proof?? I have only been doing number theory for 2 weeks now)
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    Re: can you use parity tables as proof?

    Quote Originally Posted by andychallis View Post
    can you use parity tables as proof?
    I want to use it to prove this:

    if mn is even, then at least one of m or n is even.
    I am not sure what you mean by "can you use parity tables"

    But you can prove the contrapositive.
    If both m and n are odd then mn is odd..
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  3. #3
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    Re: can you use parity tables as proof?

    m|n|mn
    E|E|E
    E|D|E
    D|E|E
    D|D|D

    so when mn is even then 'm or n' must be even
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    Re: can you use parity tables as proof?

    Quote Originally Posted by andychallis View Post
    m|n|mn
    E|E|E
    E|D|E
    D|E|E
    D|D|D

    so when mn is even then 'm or n' must be even
    I suspect that is strictly up to the instructor.
    I would not use on a number theory question. But that is my view.
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    Re: can you use parity tables as proof?

    How did you get the values in your parity table? That is, how do you know the line "D D D"?
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    Re: can you use parity tables as proof?

    because m and n can be EE ED DE or DD, E=even D=odd, there are no other cases.
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    Re: can you use parity tables as proof?

    Quote Originally Posted by andychallis View Post
    because m and n can be EE ED DE or DD, E=even D=odd, there are no other cases.
    But my point is still this is a number theory study.
    Have you proved each of those?
    If you have, then you have proved the contrapositive.
    Which means you have proved the theorem.
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