Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.3 Truth Tables for Negation, Conjunction and Disjunction - Exercise Set 3.3: 26

Answer

$\begin{array}{llll} p & q & \sim q & \sim q\wedge p\\ \hline T & T & F & F\\ T & F & T & T\\ F & T & F & F\\ F & F & T & F \end{array}$

Work Step by Step

Set up a truth table for two inputs, p and q: $\begin{array}{llll} p & q & ... & ...\\ \hline T & T & & \\ T & F & & \\ F & T & & \\ F & F & & \end{array}$ Fill column for $\sim q$, using the truth table for negation, $\begin{array}{llll} p & q & \sim q & ...\\ \hline T & T & F & \\ T & F & T & \\ F & T & F & \\ F & F & T & \end{array}$ Now, use the conjunction truth table when columns 3 and 1 give inputs (true only when both are true) $\begin{array}{llll} p & q & \sim q & \sim q\wedge p\\ \hline T & T & F & F\\ T & F & T & T\\ F & T & F & F\\ F & F & T & F \end{array}$
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