# Chapter 3 - Logic - 3.6 Negations of Conditional Statements and De Morgan's Law - Exercise Set 3.6 - Page 179: 68

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.”

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