# Math Help - Verifying using propositional equivalences - HELP

1. ## 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

2. $\begin{gathered}
\neg \left( {p \leftrightarrow q} \right) \hfill \\
\neg \left[ {\left( {p \to q} \right) \wedge \left( {q \to p} \right)} \right] \hfill \\
\left( {p \wedge \neg q} \right) \vee \left( {q \wedge \neg p} \right) \hfill \\
\end{gathered}$

$
\begin{gathered}
\left[ {\left( {p \wedge \neg q} \right) \vee q} \right] \wedge \left[ {\left( {p \wedge \neg q} \right) \vee \neg p} \right] \hfill \\
\left( {p \vee q} \right) \wedge \left( {\neg p \vee \neg q} \right) \hfill \\
\left( {\neg q \to p} \right) \wedge \left( {p \to \neg q} \right) \hfill \\
\left( {p \leftrightarrow \neg q} \right) \hfill \\
\end{gathered}$

3. Thank you very much for that mate, helped alot.