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Math Help - Existential Instantiation

  1. #1
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    Existential Instantiation

    I need to prove or disprove the following: Z = integers
    If x,y Z, with x=2q and y=2h+1, for some q,hZ, then $uZ such that xy=2u+1

    It seems like existential instantiation is the only way to do this. I don't know how to show it. Can I simply let h = u since addition and multiplication are closed under Z?

    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bclere View Post
    I need to prove or disprove the following: Z = integers
    If x,y Z, with x=2q and y=2h+1, for some q,hZ, then $uZ such that xy=2u+1

    It seems like existential instantiation is the only way to do this. I don't know how to show it. Can I simply let h = u since addition and multiplication are closed under Z?

    Thanks
    Hint: if x = 2q and y = 2h + 1 then xy = 2q(2h + 1) = \cdots
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  3. #3
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    existential instantiation

    = what? That doesn't show proof of anything!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bclere View Post
    = what? That doesn't show proof of anything!
    how do you figure? what i typed is everything you need

    the question you are supposed to ask yourself now is: can i write 2q(2h + 1) in the form 2u + 1 using only integers?

    if the answer is yes, then do it and hence prove the theorem

    if the answer is no, then say why you can't do it, thus disproving the theorem
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