## Thinking Mathematically (6th Edition)

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 an increase 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 hell. The given compound statement can be written in the symbolic form as $\left( p\leftrightarrow q \right)\wedge r$ 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 bi-conditional statement, it is false only when the simple statements have the different truth value. 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 false,$q$ is false, and $r$ is true. Put the truth values of $p,\text{ }q,\text{ and }r$ in symbolic form to get $\left( \text{F}\leftrightarrow \text{F} \right)\wedge \text{T}$. It can be further simplified as \begin{align} & \left( \text{F}\leftrightarrow \text{F} \right)\wedge \text{T}\equiv \text{T}\wedge \text{T} \\ & \text{ }\equiv \text{T} \\ \end{align}