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 161: 97

Answer

The provided statement makes sense.

Work Step by Step

Consider a compound statement, if \[2+2=5\],the sun rises from the east. Itcan be written in simple statements as p and q. Here, \[p\]and\[q\]represent two simple statements, represented by \[p\]: \[2+2=5\] \[q\] : The sun rises from the east. The compound statement can be written in the symbolic form as \[p\to q\] In case of a conditional statement, it is false only when the antecedent is true and the consequent is false. For all other combinations of truth values, conditional statements will be true. Here, the antecedent is false and the consequent is true; thus, the logic \[p\to q\]is true but if we reverse the antecedent and consequent then the antecedent is true and the consequent is false; therefore, the logic \[q\to p\] becomes false.
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