Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.2 Compound Statements and Connectives - Exercise Set 3.2 - Page 133: 84

Answer

\[p\vee \left( q\to \sim r \right)\]

Work Step by Step

The given compound statement can be written in simple statements as \[p,\text{ }q,\text{ and }r\]. Here, \[p,\text{ }q,\text{ and }r\] represents three simple statements. \[p\]: The lines go down. \[q\] : The transformer blows. \[r\] : We have power. Use the representation to re-write the statement as: p, or if q then not r. ‘If-then’ is represented by the symbol ‘\[\to \]’, ‘Or’ is represented by the symbol ‘\[\vee \]’, and ‘Not’ is represented by the symbol ‘\[\sim \]’. Use the symbols to write the compound statement in symbolic form as: \[p\vee \left( q\to \sim r \right)\]
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