   # Use two truth tables to show that each of the statements are equivalent. [ ( ∼ p ∧ ∼ q ) ∧ r ] ∨ [ ( p ∧ q ) ∧ ∼ r ] ∨ [ p ∧ ( q ∧ r ) ] , ( p ∧ q ) ∨ [ ( ∼ p ∧ ∼ q ) ∧ r ] ### 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 36ES
Textbook Problem
1 views

## Use two truth tables to show that each of the statements are equivalent. [ ( ∼ p ∧ ∼ q ) ∧ r ] ∨ [ ( p ∧ q ) ∧ ∼ r ] ∨ [ p ∧ ( q ∧ r ) ] , ( p ∧ q ) ∨ [ ( ∼ p ∧ ∼ q ) ∧ r ]

To determine

To calculate:

Using truth table, to show that the statement is equivalent

### Explanation of Solution

Given information:

Statement[(pq)r][(pq)r][p(qr)],(pq)[(pq)r] is given

Calculation:

Construct two truth tables and compare the results.

(1) Firstly, construct the truth table for[(pq)r][(pq)r][p(qr)] ,

Start with the standard truth table and then include p ,q columns.

(2) Now compute the truth values of[(pq)r] as follows

(3) Now compute the truth values of (pq) as follows

(4) Now compute the truth values of

[(pq)r] as follows

(5) Now compute the truth values of (qr) as follows

(6) Now compute the truth values of [p(qr)] as follows

(7) Now, form the disjunction of [(pq)r] with

[(pq)r] and place the results in the rightmost columns as follows

(8) In the last step form the disjunction of [(pq)r][(pq)r] with [p(qr)] and place the results in the rightmost columns as follows:

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
In Problems 3-6, factor by grouping. 3.

Mathematical Applications for the Management, Life, and Social Sciences

Solving Equations Find all real solutions of the equation. 63. 4x3 25x = 0

Precalculus: Mathematics for Calculus (Standalone Book)

Use the guidelines of Section 4.5 to sketch the curve. y = 4x tan x, /2 x /2

Single Variable Calculus: Early Transcendentals, Volume I

Convert the expressions in Exercises 6584 to power form. 3x1.2213x2.1

Finite Mathematics and Applied Calculus (MindTap Course List)

Proof Prove that u(vw)=(uw)v(uv)w

Calculus: Early Transcendental Functions

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 35-38, find an equation of the line that has slope m and y-intercept b. 37. m = 0; b = 5

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Change each fraction to a percent: 1340

Elementary Technical Mathematics

Prove the identity. 47. sec y cos y = tan y sin y

Single Variable Calculus: Early Transcendentals

Which is the largest? a) f(a) b) f(b) c) f(c) d) cannot tell from information given

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Explain how the mean and the standard deviation describe a distribution of scores.

Research Methods for the Behavioral Sciences (MindTap Course List) 