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Negating logical assertions

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Write down the negations of the following assertions (where m, n, a, b are natural numbers):

    a) if Coke is not worse than Pepsi then nothing Mandelson says can be trusted.
    b) [tex]\forall m \exists n\forall a\forall b (n >= m)[/tex] /\ [tex][(a=1)[/tex] \/[tex] (b=1)[/tex] \/ [tex](ab \ne n)][/tex]

    Answers:
    a) if Coke is not worse than Pepsi then everything Mandelson says can be trusted.
    b) [tex]\exists m\forall n \exists a\exists b (n < m)[/tex] \/[tex][(a \ne 1)[/tex] /\ [tex](b \ne 1)[/tex] /\ [tex](ab =n)][/tex]

    Could anyone check whenever or not these answers are correct?
     
  2. jcsd
  3. Oct 18, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since you have not said what "a", "b", "m", or "n" mean, it is impossible to tell.

    I will say this- the negation of an "if- then" implication is NOT an "if-then" implication.
     
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