   # Use two truth tables to show that each of the statements are equivalent. p ∨ ( q ∧ ∼ p ) , p ∨ q ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3.2, Problem 33ES
Textbook Problem
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## Use two truth tables to show that each of the statements are equivalent. p ∨ ( q ∧ ∼ p ) , p ∨ q

To determine

To calculate:

Using truth table, to show that the statement is equivalent

### Explanation of Solution

Given information:

Statementp(qp),pq is given

Calculation:

Construct two truth tables and compare the results.

(1) Firstly, construct the truth table forp(qp) ,

Now, construct the truth table as follows:

(2) Now, compute the truth values of (qp) as follows

(3) In the last step form the disjunction of (qp) with p and place the results in the rightmost columns as follows

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