Answer
Use the following representations to determine the symbolic form of the provided statements.
\[\begin{align}
& p:\text{ We will replace } \\
& q:\text{ We will repair the roof} \\
& r:\text{ We will sell the house} \\
\end{align}\]
The statement “We will neither replace nor repair the roof, and we will sell the house” in the symbolic form is\[\left( \tilde{\ }p\wedge \tilde{\ }q \right)\wedge r\].
The negation of \[\tilde{\ }\left( p\wedge q \right)\wedge r\] is\[\left( p\vee q \right)\vee \tilde{\ }r\].
Hence, the statement form of \[\left( p\vee q \right)\vee \tilde{\ }r\] is “We will either replace or repair the roof, or we will not sell the house.”
