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Math Help - Negation ... need to know if correct

  1. #1
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    Negation ... need to know if correct

    If K is bounded, then K is compact

    solution: if K is Not bounded, then K is not compact
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  2. #2
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    Re: Negation ... need to know if correct

    Sorry its suppose to read "If K is closed and bounded, then K is Compact"
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  3. #3
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    Re: Negation ... need to know if correct

    Quote Originally Posted by Odail View Post
    If K is bounded, then K is compact

    solution: if K is Not bounded, then K is not compact
    This is not the negation of the first statement.

    What would you do if you wanted to find a countereample to the first statement? Which properties should K possess to be a counterexample?
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    Re: Negation ... need to know if correct

    try to find and instance or example that shows even though K is bounded it is not Compact
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    Re: Negation ... need to know if correct

    Quote Originally Posted by Odail View Post
    If K is bounded, then K is compact

    solution: if K is Not bounded, then K is not compact
    If K is a man, then K is human.

    Would you then think it reasonable to conclude that

    If K is not a man, then K is not human.
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  6. #6
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    Re: Negation ... need to know if correct

    No .... if K is not a human, then K is not a man
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    Re: Negation ... need to know if correct

    Quote Originally Posted by Odail View Post
    try to find and instance or example that shows even though K is bounded it is not Compact
    Pretty much. One remark is that the negation of a statement is also a statement and not a command ("Try to find..."). Using your correction "If K is closed and bounded", the negation of the original statement would be, "K is closed and bounded but not compact".

    Quote Originally Posted by JeffM View Post
    If K is a man, then K is human.

    Would you then think it reasonable to conclude that

    If K is not a man, then K is not human.
    Apparently, the poblem is to construct the negation, not a corollary. OP: Please post the complete problem in the body of the message.
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  8. #8
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    Re: Negation ... need to know if correct

    Odail

    I have looked at several of your posts. They seem to be all over the place. We might be better able to help you if we had some clue about where these questions are coming from. Moreover, it is important to give a complete and exact statement of the problem. Is this question simply "What is the negation of 'If K is closed and bounded, then K is compact'"?
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  9. #9
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    Re: Negation ... need to know if correct

    Yes your construction of the statement is correct i made a mistake the first time i posted it ...
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  10. #10
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    Re: Negation ... need to know if correct

    The questions are basically tutorials questions that i don't have the answer to that im using to study for an exam
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  11. #11
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    Re: Negation ... need to know if correct

    Quote Originally Posted by Odail View Post
    The questions are basically tutorials questions that i don't have the answer to that im using to study for an exam
    @Odail, here is the rule:
    The negation of "If P then Q" is " P and not Q".

    $\neg \left( {P \to Q} \right) \equiv \neg \left( {\neg P \vee Q} \right) \equiv \left( {P \wedge \neg Q} \right)$
    Last edited by Plato; May 6th 2014 at 07:25 AM.
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