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Math Help - negations

  1. #1
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    negations

    Hi everyone,

    Could someone please tell me what the negation of "If and only if" would be? -p V -q :?

    Is the negation of "If T is continuous, then T is bounded" T is continuous and T is not bounded
    or T is not continuous and T is bounded.

    For the statement "I can eat dinner or go to the show," that would be "I cannot eat dinner and I cannot go to the show,right?"

    Thank you very much
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  2. #2
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    \neg \left( {p \Leftrightarrow q} \right) \equiv \left( {\neg p \wedge q} \right) \vee \left( {p \wedge \neg q} \right)<br />
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  3. #3
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    Could you tell me if this is correct based on that?

    The number x is prime only if x is odd

    P: the number x is prime
    Q: x is odd

    P arrow q. This negated would be (-P ^ Q) V (P ^ -Q) That is, it would read "The number x is not prime and q is odd or x is prime and x is not odd

    Thank you
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  4. #4
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    Quote Originally Posted by chocolatelover View Post
    The number x is prime only if x is odd
    P: the number x is prime
    Q: x is odd
    P arrow q. YES

    This negated would be (-P ^ Q) V (P ^ -Q) NO
    Just (P ^ -Q)
    See the above.
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  5. #5
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    In words this would be "The number x is prime or x is not odd," right?

    Thank you
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  6. #6
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    Quote Originally Posted by chocolatelover View Post
    In words this would be "The number x is prime or x is not odd," right?
    NO! The number x is prime and x is not odd.
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