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Thread: laws of propositional logic to simplify

  1. #1
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    laws of propositional logic to simplify

    simplify the following using laws of propositional logic:

    ~[p --> ~(p ^ q)]
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    Re: laws of propositional logic to simplify

    Quote Originally Posted by mathman11 View Post
    simplify the following using laws of propositional logic:

    ~[p --> ~(p ^ q)]
    do you know what $\neg (a \rightarrow b)$ equals?
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    Re: laws of propositional logic to simplify

    Hello, mathman11!

    Simplify the following using laws of propositional logic:

    . . $\displaystyle \sim \big[p \to \:\sim(p \wedge q)\big]$

    $\displaystyle \begin{array}{cccccccccc}1. & \sim \big[p \to \:\sim(p \wedge q)\big] && 1. & \text{Given} \\ 2. & \sim\big[\sim p\: \vee \sim(p \wedge q)\big] && 2. & \text{Def. of Impl'n} \\ 3. & \sim\big[\sim p \vee (\sim p \:\vee \sim q)\big] && 3. & \text{DeMorgan} \\ 4. & \sim \big[(\sim p\:\vee \sim p)\:\vee \sim q\big] && 4 . & \text{Associative} \\ 5. & \sim\big(\sim p \:\vee \sim q\big) && 5. & \text{Identity prop.} \\ 6. & p \wedge q && 6. & \text{DeMorgan} \end{array}$
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    Re: laws of propositional logic to simplify

    Thanks Soroban .That helped alot.I'm having a hard time remembering the specific laws itself. What are some techniques to remember them?
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