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 159: 34

Answer

The given statement is a tautology.

Work Step by Step

A compound statement that is always true is called a Tautology, and a compound statement that is always false is called a self-contradiction. Determine the truth table for the provided statement \[\left[ \left( p\to q \right)\wedge p \right]\to q\] as shown below, As seen from the truth table that the given statement is always true, therefore, it is a tautology. Hence, the given statement is always true, therefore, it is a tautology.
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