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 statement.
\[p\]: There is an increase in the percentage who believed in God.
\[q\]: There is a decrease in the percentage who believed in Heaven.
\[r\]: There is an increase in the percentage who believed in the devil.
The given compound statement can be written in the symbolic form as
\[\left( p\wedge q \right)\to r\]
A conjunction is true only when the truth values of all simple statements are true. In all other cases of truth values, it is false. 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 true values conditional statements will be true.
From the provided bar graph, it can be observed that \[p\]is false,\[q\]is true, and\[r\]is false. Put the truth values of\[p,\text{ }q,\text{ and }r\] in symbolic form to get \[\left( \text{F}\wedge \text{T} \right)\to \text{F}\]. It can be further simplified as
\[\begin{align}
& \left( \text{F}\wedge \text{T} \right)\to \text{F}\equiv \text{F}\to \text{F} \\
& \text{ }\equiv \text{T} \\
\end{align}\]
Work Step by Step
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