Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.2 Compound Statements and Connectives - Exercise Set 3.2 - Page 134: 119

Answer

Simple statements are: p: Shooting unarmed civilians is morally justifiable, q: Bombing unarmed civilians is morally justifiable and the symbolic form of the provided compound statement is\[\left( \left( p\leftrightarrow q \right)\wedge \sim p \right)\to \sim q\].

Work Step by Step

The compound statement is “Shooting unarmed civilians is morally justifiable if and only if bombing them is morally justifiable, and as the former is not morally justifiable, neither is the latter”. Firstly, assign the letters the simple statements which are not negated. Now, the simple statements are: p: Shooting unarmed civilians is morally justifiable, q: Bombing unarmed civilians is morally justifiable. The disjunction statement is: \[p\vee q\]: \[p\] Or \[q\]. The conditional statement is: \[p\to q\]: If\[p\], then \[q\]. The Bi conditional statement is: \[p\leftrightarrow q\]: \[p\]If and only if \[q\]. Use the above all definitions then the symbolic form of the provided compound statement is\[\left( \left( p\leftrightarrow q \right)\wedge \sim p \right)\to \ \sim q\].
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