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Math Help - IS this proof valid or invalid?

  1. #1
    Newbie Crayola's Avatar
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    IS this proof valid or invalid?

    IS this proof valid or invalid?-captures.png

    I attached a picture of the proof. Any help is appreciated!
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  2. #2
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    Re: IS this proof valid or invalid?

    Quote Originally Posted by Crayola View Post
    Click image for larger version. 

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    I attached a picture of the proof. Any help is appreciated!
    Maybe it just my browser, but I see absolutely no proof in that link.

    In any case this is true: \neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]
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    Re: IS this proof valid or invalid?

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  4. #4
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    Re: IS this proof valid or invalid?

    Quote Originally Posted by Plato View Post
    Maybe it just my browser, but I see absolutely no proof in that link.

    In any case this is true: \neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]
    Right, sorry I meant statement. So why wouldn't the given be valid?
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    Re: IS this proof valid or invalid?

    Quote Originally Posted by Crayola View Post
    Right, sorry I meant statement. So why wouldn't the given be valid?
    On the set of all real numbers, let P(x) mean “x is positive”.

    \neg \left( {\forall x} \right)\left[ {P(x)} \right] means “Some real number is not positive”. Literally, “It is false that all real numbers are positive”.

    Whereas, \left( {\forall x} \right)\left[ {\neg P(x)} \right] means “No real number is positive”. Literally, “All real numbers are not positive”.

    Now can you answer the question?
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  6. #6
    Newbie Crayola's Avatar
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    Re: IS this proof valid or invalid?

    Okay, thank you!
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