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# Explain, without using a truth table, why (p q r ) (¬ p ¬ ISBN: 9780073383095 37

## Solution for problem 41E Chapter 1.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 41E

Explain, without using a truth table, why (p ? q ? r ) ? (¬ p ? ¬ q) is true when at least one of p, q , and r is true and at least one is false, but is false when all three variables have the same truth value.

Step-by-Step Solution:
Step 1 of 3

Solution: Step-1: In this problem we need to explain without using a truth table , is true. Given: is true. When at least one of p , q, and r is true and at least one is false , but is false when all three variables have the same truth value. Conjunction : If p and q are statements , then the statement is true only when both p and q are true , and is false otherwise. Disjunction: If p and q are statements , then the statement is true when at least one of the two statements is true , and is false when both are false.Step-2: By using the above definitions : If at least one of p , q, and r is true if and only if the result is true. …………….(1) If at least one of p , q, and r is false if and only if the result is true. ……………..(2) From (1) , (2) it is clear that the entire statement is true if and only if there is at least one true and one false. So ,the given statement is false when all three variables have the same truth value.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The answer to “Explain, without using a truth table, why (p ? q ? r ) ? (¬ p ? ¬ q) is true when at least one of p, q , and r is true and at least one is false, but is false when all three variables have the same truth value.” is broken down into a number of easy to follow steps, and 51 words. This full solution covers the following key subjects: true, False, least, truth, explain. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 41E from 1.1 chapter was answered, more than 352 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 41E from chapter: 1.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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Explain, without using a truth table, why (p q r ) (¬ p ¬