Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.5 Equivalent Statements and Variations of Conditional Statements - Exercise Set 3.5 - Page 170: 1

Answer

(a) Determine the truth table for \[\sim p\to q\] and \[p\vee q\] as shown below, It can be seen from the truth table that the values of \[\sim p\to q\] and \[p\vee q\] are same. (b) Use the following statement to determine symbolic representation of the provided statement, p: The United states energetically support the development of solar-powered cars. q: It will suffer increasing atmospheric pollution. The given statement can be represented in symbolic form as,\[\sim p\to q\]. In part (a) it has been shown that \[\sim p\to q\] and \[p\vee q\] are equivalent. Therefore, the statement that is equivalent to the provided statement is, The United states energetically support the development of solar-powered cars or it will suffer increasing atmospheric pollution.
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