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Math Help - 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 :

    <br />
 p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)<br />

    I Have tried this out :

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

    <br />
 p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)<br />

    I Have tried this out :

    <br />
p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)<br />
    p \Leftrightarrow q means p \Rightarrow q and q \Rightarrow p.


    From the contrapositive:

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

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


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