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Determine the negation of the expression

  1. Sep 1, 2011 #1
    The question states:

    Determine the negation of the expression.

    p -> q ^ r.

    I am having difficulty finding the negation. Below are the steps I have taken in an attempt to come to the solution.

    The - symbol will be the negate symbol.

    p -> q ^ r

    (-p OR q) ^ r

    -(-p OR q) ^ r

    (p ^ -q) ^ r

    -((p ^ -q) ^ r)

    -p OR - r OR q

    -(p ^ r) OR q

    I feel like I am going in circles. I have made truth tables to compare but have had no luck. Please any advise would be appreciated.
     
  2. jcsd
  3. Sep 1, 2011 #2
    Re: Logic

    If you look at a truth table for a conditional statement such as [itex]P\rightarrow Q[/itex], you should find that the only time this statement is rendered false is if the antecedent (the first part, [itex]P[/itex]) is true and the consequent (the second part, [itex]Q[/itex]) is false.

    So, what does that tell you about your problem? Keep the antecedent as it is, and negate the consequent, [itex](Q\wedge R)[/itex].
     
  4. Sep 14, 2011 #3
    Re: Logic

    Thank you!
     
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