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Math Help - ~(p ► q)

  1. #1
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    ~(p ► q)

    If p = My dog swims and q = the water is cold, what is ~(p ► q)? is it my dog swims if the water isn't cold?
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  2. #2
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    Hello, Kathryn!

    \begin{array}{ccc}p &=& \text{my dog swims} \\ q &=& \text{the water is cold}\end{array}

    What is: . \sim (p \to q) ?

    We know that: . p \to q \;\;\Longleftrightarrow\;\;\sim\!p \vee q

    Then: . \sim(p \to q)\;\;\Longleftrightarrow\;\;\sim(\sim\!p \vee q) \;\;\Longleftrightarrow\;\;p \:\wedge \sim\! q .
    DeMorgan's Law


    In English: .My dog swims and the water is not cold.

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