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Math Help - Can one negate whenever they want?

  1. #1
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    Can one negate whenever they want?

    When trying to prove a logical equivalence, are you allowed to negate when you want?

    For example am I allowed to do this
    (a \wedge b)
    <=>
    \neg a \vee \neg b
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  2. #2
    Junior Member
    Joined
    Sep 2011
    Posts
    58

    Re: Can one negate whenever they want?

    You can always substitute a statement with a logically equivalent statement if that's your question.

    The two statements you have listed are not logically equivalent so you CANNOT substitute them for each other.

    If you have an equivalence like p\Leftrightarrow q then you are allowed to negate both sides and say \neg p \Leftrightarrow \neg q because the statements are logically equivalent

    (by logically equivalent I mean that if you wrote out truth tables, the values in the two columns would be identical)
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