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 134: 94

Answer

Simple statements are: p: Falling in love with someone in your class. q: Picking someone to hate. r: Vent your emotions. s: skip. Symbolic form is \[\left( p\vee q \right)\to \left( r\wedge \tilde{\ }s \right)\]

Work Step by Step

The given compound statement can be written in simple statements as \[p,\text{ }q,\text{ }r,\text{ and }s\]. Here, \[p,\text{ }q,\text{ }r,\text{ and }s\] represents three simple statements. p: You fall in love with someone in your class. q: You pick someone to hate. r: You show up to vent your emotions. s: You skip. Use the representation to re-write the statement as: p or q are sufficient conditions for r and not s. ‘Sufficient conditions’ is represented by the symbol ‘\[\to \]’, ‘And’ is represented by the symbol ‘\[\wedge \]’, ‘Not’ is represented by the symbol ‘\[\sim \]’, and ‘Or’ is represented by the symbol ‘\[\vee \]’. Use the symbols to write the compound statement in symbolic form as: \[\left( p\vee q \right)\to \left( r\wedge \tilde{\ }s \right)\]
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