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: 69


Use the following representations to determine the symbolic form of the provided statements. \[\begin{align} & \text{ }p:\text{ it is Thanksgiving} \\ & q:\text{ people eating turkey} \\ \end{align}\] The statement “Some people eating turkey is necessary for it to be Thanksgiving” in the symbolic form is\[p\to q\]. The contra positive of \[p\to q\] is\[\sim q\to \sim p\]. Hence, the statement form of \[\sim q\to \sim p\] is “If no one is eating turkey, then it is not Thanksgiving.” The negation of \[p\to q\] is\[p\wedge \sim q\]. Hence, the statement form of \[p\wedge \sim q\] is “It is Thanksgiving and no one is eating turkey.”
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