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Math Help - Verifying using propositional equivalences - HELP

  1. #1
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    Unhappy Verifying using propositional equivalences - HELP

    Hey can anyone help me with this equation: (need to verify using equivalences)

    not(p ↔ q )

    The answer to this should be (p ↔ not q) but I dont know how to get there step by step.

    Help any one?

    Thanks
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  2. #2
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    \begin{gathered}<br />
  \neg \left( {p \leftrightarrow q} \right) \hfill \\<br />
  \neg \left[ {\left( {p \to q} \right) \wedge \left( {q \to p} \right)} \right] \hfill \\<br />
  \left( {p \wedge \neg q} \right) \vee \left( {q \wedge \neg p} \right) \hfill \\ <br />
\end{gathered}
    <br />
\begin{gathered}<br />
  \left[ {\left( {p \wedge \neg q} \right) \vee q} \right] \wedge \left[ {\left( {p \wedge \neg q} \right) \vee \neg p} \right] \hfill \\<br />
  \left( {p \vee q} \right) \wedge \left( {\neg p \vee \neg q} \right) \hfill \\<br />
  \left( {\neg q \to p} \right) \wedge \left( {p \to \neg q} \right) \hfill \\<br />
  \left( {p \leftrightarrow \neg q} \right) \hfill \\ <br />
\end{gathered}
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  3. #3
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    Talking

    Thank you very much for that mate, helped alot.

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