Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

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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