Question

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

Solution

VerifiedStep 1

1 of 2According 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

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences

14th Edition•ISBN: 9780134675985 (3 more)Christopher J. Stocker, Karl E. Byleen, Michael R. Ziegler, Raymond A. Barnett3,808 solutions

#### Finite Mathematics

11th Edition•ISBN: 9780321979438Margaret L. Lial, Nathan P. Ritchey, Raymond N. Greenwell5,113 solutions

#### Mathematical Excursions

4th Edition•ISBN: 9781305965584Daniel K. Clegg, Joanne Lockwood, Richard D. Nation, Richard N. Aufmann4,593 solutions

## More related questions

1/4

1/7