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.
\[p\]: 15% are capitalists.
\[q\]: 34% are members of the upper-middle class.
\[r\]: The number of working poor exceeds the number belonging to the working class.
The given compound statement can be written in the symbolic form as
\[\left( p\vee \sim q \right)\leftrightarrow r\]
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 different truth values. However, if they have same truth values which is either both true or false, then the resultant truth value is true. Further, negation can be done by finding the complement of the truth values.
From the provided bar graph, it can be observed that \[p\] is false,\[q\] is false, and \[r\] is false. Put the truth values of \[p,\text{ }q,\text{ and }r\] in symbolic form to get \[\left( \text{F}\vee \sim \text{F} \right)\leftrightarrow \text{F}\]. It can be further simplified as
\[\begin{align}
& \left( \text{F}\vee \sim \text{F} \right)\leftrightarrow \text{F}\equiv \text{T}\leftrightarrow \text{F} \\
& \text{ }\equiv \text{F} \\
\end{align}\]
Work Step by Step
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