Explanation The given argument has three, premises i.e. “If (p or q), then Not r”, “p or Not q” and “If Not q, then p” and “Not r”, is the conclusion. The truth table has been prepared as below, the table is obtained by considering the eight possible combinations of truth values for p, q and r as provided at column 1 , 2 & 3 of the truth table respectively. The truth values for the whole premise statement has been placed in columns 7 , 8 & 9 providing “If (p or q), then Not r”, “p or Not q” and “If Not q, then p” respectively and the same have been shown in the table. The tenth column represents the truth values of the conclusion i.e. “Not r”. It can be seen from the truth table that there are three situations/ rows where all the three premise are true and hence the three rows, i.e. 2 n d , 3 r d & 4 t h rows become the CRITICAL ROWS . Premises Conclusion p q r ∼ q p ∧ q ∼ r p ∧ q → ∼ r p ∨ ( ∼ q ) ∼ q → p ∼ r T T T F T F F T T

Discrete Mathematics: Introduction to Mathematical Reasoning

1st Edition

ISBN: 9780495826170

Author: Susanna S. Epp

Publisher: Cengage Learning

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Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

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Chapter 2.3, Problem 9ES

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To test the argument form for its validity using Truth Tables.

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Chapter 2 Solutions

Discrete Mathematics: Introduction to Mathematical Reasoning

Ch. 2.1 - Prob. 1ES Ch. 2.1 - Prob. 2ES Ch. 2.1 - Prob. 3ES Ch. 2.1 - Prob. 4ES Ch. 2.1 - Prob. 5ES Ch. 2.1 - Prob. 6ES Ch. 2.1 - Prob. 7ES Ch. 2.1 - Prob. 8ES Ch. 2.1 - Prob. 9ES Ch. 2.1 - Prob. 10ES

Ch. 2.1 - Prob. 11ES Ch. 2.1 - Prob. 12ES Ch. 2.1 - Prob. 13ES Ch. 2.1 - Prob. 14ES Ch. 2.1 - Prob. 15ES Ch. 2.1 - Prob. 16ES Ch. 2.1 - Prob. 17ES Ch. 2.1 - Prob. 18ES Ch. 2.1 - Prob. 19ES Ch. 2.1 - Prob. 20ES Ch. 2.1 - Prob. 21ES Ch. 2.1 - Prob. 22ES Ch. 2.1 - Prob. 23ES Ch. 2.1 - Prob. 24ES Ch. 2.1 - Prob. 25ES Ch. 2.1 - Prob. 26ES Ch. 2.1 - Prob. 27ES Ch. 2.1 - Prob. 28ES Ch. 2.1 - Prob. 29ES Ch. 2.1 - Prob. 30ES Ch. 2.1 - Prob. 31ES Ch. 2.1 - Prob. 32ES Ch. 2.1 - Prob. 33ES Ch. 2.1 - Prob. 34ES Ch. 2.1 - Prob. 35ES Ch. 2.1 - Prob. 36ES Ch. 2.1 - Prob. 37ES Ch. 2.1 - Prob. 38ES Ch. 2.1 - Prob. 39ES Ch. 2.1 - Prob. 40ES Ch. 2.1 - Prob. 41ES Ch. 2.1 - Prob. 42ES Ch. 2.1 - Prob. 43ES Ch. 2.1 - Prob. 44ES Ch. 2.1 - Prob. 45ES Ch. 2.1 - Prob. 46ES Ch. 2.1 - Prob. 47ES Ch. 2.2 - Prob. 1ES Ch. 2.2 - Prob. 2ES Ch. 2.2 - Prob. 3ES Ch. 2.2 - Prob. 4ES Ch. 2.2 - Prob. 5ES Ch. 2.2 - Prob. 6ES Ch. 2.2 - Prob. 7ES Ch. 2.2 - Prob. 8ES Ch. 2.2 - Prob. 9ES Ch. 2.2 - Prob. 10ES Ch. 2.2 - Prob. 11ES Ch. 2.2 - Prob. 12ES Ch. 2.2 - Prob. 13ES Ch. 2.2 - Prob. 14ES Ch. 2.2 - Prob. 15ES Ch. 2.2 - Prob. 16ES Ch. 2.2 - Prob. 17ES Ch. 2.2 - Prob. 18ES Ch. 2.2 - Prob. 19ES Ch. 2.2 - Prob. 20ES Ch. 2.2 - Prob. 21ES Ch. 2.2 - Prob. 22ES Ch. 2.2 - Prob. 23ES Ch. 2.2 - Prob. 24ES Ch. 2.2 - Prob. 25ES Ch. 2.2 - Prob. 26ES Ch. 2.2 - Prob. 27ES Ch. 2.2 - Prob. 28ES Ch. 2.2 - Prob. 29ES Ch. 2.2 - Prob. 30ES Ch. 2.2 - Prob. 31ES Ch. 2.2 - Prob. 32ES Ch. 2.2 - Prob. 33ES Ch. 2.2 - Prob. 34ES Ch. 2.2 - Prob. 35ES Ch. 2.2 - Prob. 36ES Ch. 2.2 - Prob. 37ES Ch. 2.2 - Prob. 38ES Ch. 2.2 - Prob. 39ES Ch. 2.2 - Prob. 40ES Ch. 2.2 - Prob. 41ES Ch. 2.2 - Prob. 42ES Ch. 2.2 - Prob. 43ES Ch. 2.2 - Prob. 44ES Ch. 2.2 - Prob. 45ES Ch. 2.2 - Prob. 46ES Ch. 2.3 - Prob. 1ES Ch. 2.3 - Prob. 2ES Ch. 2.3 - Prob. 3ES Ch. 2.3 - Prob. 4ES Ch. 2.3 - Prob. 5ES Ch. 2.3 - Prob. 6ES Ch. 2.3 - Prob. 7ES Ch. 2.3 - Prob. 8ES Ch. 2.3 - Prob. 9ES Ch. 2.3 - Prob. 10ES Ch. 2.3 - Prob. 11ES Ch. 2.3 - Prob. 12ES Ch. 2.3 - Prob. 13ES Ch. 2.3 - Prob. 14ES Ch. 2.3 - Prob. 15ES Ch. 2.3 - Prob. 16ES Ch. 2.3 - Prob. 17ES Ch. 2.3 - Prob. 18ES Ch. 2.3 - Prob. 19ES Ch. 2.3 - Prob. 20ES Ch. 2.3 - Prob. 21ES Ch. 2.3 - Prob. 22ES Ch. 2.3 - Prob. 23ES Ch. 2.3 - Prob. 24ES Ch. 2.3 - Prob. 25ES Ch. 2.3 - Prob. 26ES Ch. 2.3 - Prob. 27ES Ch. 2.3 - Prob. 28ES Ch. 2.3 - Prob. 29ES Ch. 2.3 - Prob. 30ES Ch. 2.3 - Prob. 31ES Ch. 2.3 - Prob. 32ES Ch. 2.3 - Prob. 33ES Ch. 2.3 - Prob. 34ES Ch. 2.3 - Prob. 35ES Ch. 2.3 - Prob. 36ES Ch. 2.3 - Prob. 37ES Ch. 2.3 - Prob. 38ES Ch. 2.3 - Prob. 39ES Ch. 2.3 - Prob. 40ES Ch. 2.3 - Prob. 41ES Ch. 2.3 - Prob. 42ES Ch. 2.3 - Prob. 43ES Ch. 2.3 - Prob. 44ES

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To test the argument form for its validity using Truth Tables.

Solution Summary: The author explains that the truth table is prepared to test the argument form for its validity using Truth Tables.

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Chapter 2 Solutions