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: 61

Answer

To form the negation of a conditional statement, leave the antecedent (the first part) unchanged, change the if-then connective to, and negate the consequent (the second part). Example: The negation of given statement is “I am in Los Angeles and not in California.” To form the negation of a conditional statement, leave the antecedent (the first part unchanged, change the \[\text{if-then}\] connective to and) and negate the consequent the second part. By using following representation in statement, \[p:\] I am in Los Angeles. \[q:\] I am in California. Symbolic representation of statement is\[p\to q\]. Then negation of \[p\to q\] is \[p\wedge \sim q\] The statement form of \[p\wedge \sim q\] is “If I am in Los Angeles and I am not in California.” The negation of provided conditional statement is “If I am in Los Angeles and I am not in California.”
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