Explanation Given Information: The provided statement is ∼ ( p ∧ ( ∼ q ) ) ≡ ( ∼ p ) ∨ q . Formula used: The symbol ( ≡ ) implies logical equivalence which means that right-hand side statement is logically equivalent to the left-hand side statement and both the statement have the same truth values. The symbol ∧ implies conjunction which means that if both the statements are true then the conclusion of the statements will be true otherwise false. The symbol ∨ implies disjunction which means that if either of the two statements is true or both statements are true then the conclusion of the statements will be true. Proof: Consider the statement ∼ ( p ∧ ( ∼ q ) ) ≡ ( ∼ p ) ∨ q . There are two variables and q . So, the first two columns of the table are for the two variables, the fourth column represents p ∧ ( ∼ q ) , the fifth column represents ∼ ( p ∧ ( ∼ q ) ) and the seventh column represents ( ∼ p ) ∨ q as the given statement requires ∼ ( p ∧ ( ∼ q ) ) ≡ ( ∼ p ) ∨ q

7th Edition

ISBN: 8220103612005

Author: Costenoble

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter A, Problem 68E

To determine

To prove: The logical equivalence of ∼(p∧(∼q))≡(∼p)∨q by use of the truth table.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter A, Problem 67E

Chapter A, Problem 69E

Students have asked these similar questions

If h(x) = -2x-8 49x2-9 what is lim h(x)? x--00

Question Find the following limit. Select the correct answer below: ○ 0 ○ 3 ○ 6 ∞ 6x + 3e lim 00+2 x 2

What is the limit as x → ∞ of t(x) = = √81x2 -3x+5

Chapter A Solutions

EBK FINITE MATH AND APPLIED CALCULUS

Ch. A - Prob. 1E Ch. A - Prob. 2E Ch. A - Prob. 3E Ch. A - Prob. 4E Ch. A - Prob. 5E Ch. A - Prob. 6E Ch. A - Prob. 7E Ch. A - Prob. 8E Ch. A - Prob. 9E Ch. A - Prob. 10E

Ch. A - Prob. 11E Ch. A - Prob. 12E Ch. A - Prob. 13E Ch. A - Prob. 14E Ch. A - Prob. 15E Ch. A - Prob. 16E Ch. A - Prob. 17E Ch. A - Let p: Willis is a good teacher, q: Carla is a...Ch. A - Prob. 19E Ch. A - Let p: Willis is a good teacher, q: Carla is a...Ch. A - Prob. 21E Ch. A - Prob. 22E Ch. A - Let p: Willis is a good teacher, q: Carla is a...Ch. A - Prob. 24E Ch. A - Prob. 25E Ch. A - Prob. 26E Ch. A - Prob. 27E Ch. A - Assume that it is true that Polly sings well, it...Ch. A - Assume that it is true that Polly sings well, it...Ch. A - Prob. 30E Ch. A - Prob. 31E Ch. A - Prob. 32E Ch. A - Prob. 33E Ch. A - Prob. 34E Ch. A - Prob. 35E Ch. A - Prob. 36E Ch. A - Prob. 37E Ch. A - Prob. 38E Ch. A - Prob. 39E Ch. A - Prob. 40E Ch. A - Prob. 41E Ch. A - Prob. 42E Ch. A - Prob. 43E Ch. A - Prob. 44E Ch. A - Find the truth value of each of the statements in...Ch. A - Prob. 46E Ch. A - Prob. 47E Ch. A - Prob. 48E Ch. A - Prob. 49E Ch. A - Prob. 50E Ch. A - Prob. 51E Ch. A - Prob. 52E Ch. A - Prob. 53E Ch. A - Prob. 54E Ch. A - Prob. 55E Ch. A - Prob. 56E Ch. A - Prob. 57E Ch. A - Prob. 58E Ch. A - Prob. 59E Ch. A - Prob. 60E Ch. A - Prob. 61E Ch. A - Prob. 62E Ch. A - Prob. 63E Ch. A - Prob. 64E Ch. A - Use truth tables to verify the logical...Ch. A - Prob. 66E Ch. A - Use truth tables to verify the logical...Ch. A - Prob. 68E Ch. A - Prob. 69E Ch. A - Prob. 70E Ch. A - Prob. 71E Ch. A - Prob. 72E Ch. A - Prob. 73E Ch. A - Prob. 74E Ch. A - Prob. 75E Ch. A - Prob. 76E Ch. A - Prob. 77E Ch. A - Prob. 78E Ch. A - Prob. 79E Ch. A - Prob. 80E Ch. A - Prob. 81E Ch. A - Prob. 82E Ch. A - Prob. 83E Ch. A - Prob. 84E Ch. A - Prob. 85E Ch. A - Prob. 86E Ch. A - Prob. 87E Ch. A - Prob. 88E Ch. A - Prob. 89E Ch. A - Give the contrapositive and converse of each of...Ch. A - Prob. 91E Ch. A - Prob. 92E Ch. A - Prob. 93E Ch. A - Prob. 94E Ch. A - Prob. 95E Ch. A - Prob. 96E Ch. A - Prob. 97E Ch. A - Prob. 98E Ch. A - Prob. 99E Ch. A - Prob. 100E Ch. A - Prob. 101E Ch. A - Prob. 102E Ch. A - Prob. 103E Ch. A - Prob. 104E Ch. A - Prob. 105E Ch. A - Prob. 106E Ch. A - Prob. 107E Ch. A - Prob. 108E Ch. A - Prob. 109E Ch. A - Prob. 110E Ch. A - Prob. 111E Ch. A - Prob. 112E Ch. A - Prob. 113E Ch. A - Prob. 114E Ch. A - Prob. 115E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To prove: The logical equivalence of ∼ ( p ∧ ( ∼ q ) ) ≡ ( ∼ p ) ∨ q by use of the truth table.

Solution Summary: The author demonstrates the logical equivalence of sim 'left' by using the truth table.

Concept explainers

Videos

To prove: The logical equivalence of ∼(p∧(∼q))≡(∼p)∨q by use of the truth table.

Want to see the full answer?

Chapter A Solutions