Answer
The symbolic form is \[\left( p\vee q \right)\wedge \tilde{\ }r\] and truth value is true.
Work Step by Step
Assume the statement:
\[p\]: 7.9% named teaching.
\[q\]: 6.9% named nursing.
\[r\]: 12% named business.
The symbol ‘~’ is used for the word ‘not’, ‘\[\vee \]’ for the word ‘or’, and ‘\[\wedge \]’ for ‘and’.
So, combine all the simple statements to write the compound statement in symbolic form by the use of the symbols ‘~’, ‘\[\vee \]’ and ‘\[\wedge \]’.
The symbolic form of the statement “7.9% named teaching or 6.9% named nursing, and it is not true that 12% named the business” is \[\left( p\vee q \right)\wedge \tilde{\ }r\].
Now from given graph:
The statement \[p\] is true, the statement \[q\] is false and the statement \[r\]is false.
Consider the statement:
\[\left( p\vee q \right)\wedge \tilde{\ }r\]
Substitute the truth value true as T and false as F and use properties of conjunction and disjunction (conjunction gives truth value true only when all statements are true and disjunction gives truth value false only when all statements are false, and also use the negation property to make the statement negative).
\[\begin{align}
& \left( \text{T}\vee \text{F} \right)\wedge \tilde{\ }\text{F} \\
& \text{T}\wedge \text{T} \\
& \text{T} \\
\end{align}\]
