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: 54


Consider the symbolic form of the conditional statement as \[p\vee \left( \sim r\to s \right)\]. Here \[\sim r\] is antecedent. Use De Morgan’s law to negate the conjunction negate each component and change \[\wedge \] to \[\vee \] and change \[\to \] to \[\wedge \]. The negation of \[p\vee \left( \sim r\to s \right)\] is \[\sim p\wedge \left( \sim r\wedge \sim s \right)\].
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