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Explain, without using a truth table, is true when p ,q,

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 40E Chapter 1.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 40E

Explain, without using a truth table, is true when p ,q, and r have the same truth value and it is false otherwise.

Step-by-Step Solution:
Step 1 of 3

 Step-1:

  In this problem we need to explain without  using a truth table , is true when p,q and r have the same truth value and it is false otherwise.

  Given: is true. When p , q, and r have the same truth value  and it is false otherwise.

 Conjunction : If p and q are statements , then the statement  (read p and q)  is true  only when both p and q are true , and is false otherwise.

 Disjunction:  If p and q are statements , then the statement (read p or q)  is true  when at least  one of the two statements  is true , and is false when both are false.

Negation:Let P stand for a given statement.Thenrepresents the logical opposite of P. When P is true, then  is false and vice versa.

Step-2:

  By  using the above definitions :

     If p , q, and r have the same truth value then  ,  ,and  are true. Since by  disjunction definition .  

 ...

Step 2 of 3

Chapter 1.1, Problem 40E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Explain, without using a truth table, is true when p ,q,

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