Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.4 Truth Tables for the Conditional and the Biconditional - Exercise Set 3.4 - Page 160: 65

Answer

The truth value of the provided compound statement with the provided condition is false

Work Step by Step

The provided compound statement in symbolic form is\[\sim \left( p\to q \right)\]. Substitute the truth values for simple statements\[p,q,r\] to determine the truth value for the provided compound statement\[\sim \left( p\to q \right)\]. The provided compound statement is a negation of\[\left( p\to q \right)\], which is a conditional statement. A conditional statement is false only when the antecedent is true and the consequent is false. In all other cases, it is true. Replace with the truth values of a simple statement, \[\sim \left( \text{F}\to \text{T} \right)\]. This implies the truth values can be rewritten as \[\sim \left( \text{T} \right)\] or in the simplest form, it can be written as false. Therefore, it can be represented in the table form as:
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