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Question

# Verify each equivalence using formulas from Table 2. $p \rightarrow \neg q \equiv \neg(p \wedge q)$

Solution

Verified
Step 1
1 of 2

According to given table we know:

• $\neg(\neg p) \equiv p$
• $p \lor q \equiv q \lor p$
• $p \land q \equiv q \land p$
• $p \rightarrow q \equiv \neg p \lor q$
• $\neg(p \lor q) \equiv \neg q \land \neg p$
• $\neg(p \land q) \equiv \neg q \lor \neg p$
• $p \rightarrow q \equiv \neg q \rightarrow \neg p$

Simplifying $p \rightarrow \neg q$:

\begin{align*} p \rightarrow \neg q &= \neg p \lor \neg q\\ &=\textcolor{#4257b2}{ \neg(p \land q) } \end{align*}

As both sides are identical, hence equivalence is proved

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