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Thread: How to Prove this WFF

  1. #1
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    Tehran
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    Cool How to Prove this WFF

    Hi Help To Prove this :

    $\displaystyle
    p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)
    $

    I Have tried this out :

    $\displaystyle
    p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)
    $
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  2. #2
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    Quote Originally Posted by parkhid View Post
    Hi Help To Prove this :

    $\displaystyle
    p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)
    $

    I Have tried this out :

    $\displaystyle
    p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)
    $
    $\displaystyle p \Leftrightarrow q$ means $\displaystyle p \Rightarrow q$ and $\displaystyle q \Rightarrow p$.


    From the contrapositive:

    If $\displaystyle p \Rightarrow q$ then $\displaystyle (\sim q) \Rightarrow (\sim p)$.

    If $\displaystyle q \Rightarrow p$ then $\displaystyle \sim p \Rightarrow (\sim q)$.


    Therefore $\displaystyle p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)$.
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