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: 85

Answer

The given compound statement can be written in simple statements as \[p,\text{ }q,\text{ and }r\].Here, \[p,\text{ }q,\text{ and }r\] represent three simple statements. \[p\]: There is a decrease in the percentage who believed in God. \[q\]: There is an increase in the percentage who believed in Heaven. \[r\]: There is a decrease in the percentage who believed in the devil. The given compound statement can be written in the symbolic form as \[\left( p\leftrightarrow q \right)\vee r\] A disjunction is false only when the truth values of all simple statements are false. In all other cases of truth values, it is true. In case of a biconditional statement, it is false only when the simple statements have different truth values. However, if they have same truth values which is either both true or false, then the resultant truth value is true. From the provided bar graph, it can be observed that \[p\] is true,\[q\] is false, and \[r\] is true. Put the truth values of \[p,\text{ }q,\text{ and }r\] in symbolic form to get \[\left( \text{T}\leftrightarrow \text{F} \right)\vee \text{T}\]. It can be further simplified as \[\begin{align} & \left( \text{T}\leftrightarrow \text{F} \right)\vee \text{T}\equiv \text{F}\vee \text{T} \\ & \text{ }\equiv \text{T} \\ \end{align}\]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.