Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.3 - Propositional Equivalences - Exercises - Page 34: 5

Answer

$\left[\begin{array}{lll} p & q & r\\ \hline & & \\ T & T & T\\ T & T & F\\ T & F & T\\ T & F & F\\ F & T & T\\ F & T & F\\ F & F & T\\ F & F & F \end{array}\right.$ $\left.\begin{array}{lll} q\vee r & & p\wedge(q\vee r\\ \hline & & \\ T & & T\\ T & & T\\ T & & T\\ F & & F\\ T & & F\\ T & & F\\ T & & F\\ F & & F \end{array}\right]$ $\left[\begin{array}{lll} p & q & r\\ \hline & & \\ T & T & T\\ T & T & F\\ T & F & T\\ T & F & F\\ F & T & T\\ F & T & F\\ F & F & T\\ F & F & F \end{array}\right. \left.\begin{array}{lll} p\wedge q & p\wedge r & (p\wedge q)\vee(p\wedge r)\\ \hline & & \\ T & T & T\\ T & F & T\\ F & T & T\\ F & F & F\\ F & F & F\\ F & F & F\\ F & F & F\\ F & F & F \end{array}\right]$

Work Step by Step

The columns for $p\wedge(q\vee r)$ and $(p\wedge q)\vee(p\wedge r)$ are identical.
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