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 1.1 - Propositional Logic - Exercises - Page 15: 35

Answer

See step by step work for solution.

Work Step by Step

a) $p \to \neg q$ \begin{array}{c|c|c} p & q & p \to \neg q& \\ T & T & F \\ T & F & T \\ F & T & T \\ F & F & T \\ \end{array} b) $\neg p \leftrightarrow q$ \begin{array}{c|c|c} p & q & \neg p \leftrightarrow q& \\ T & T & F \\ T & F & T \\ F & T & T \\ F & F & F \\ \end{array} c) $(p \to q) \lor (\neg p \to q)$ \begin{array}{c|c|c} p & q & p \to q & \neg p \to q& (p \to q) \lor (\neg p \to q) \\ T & T & T&T &T \\ T & F & F&T &T\\ F & T & T& T &T\\ F & F & T& F&T\\ \end{array} d)$(p \to q) \land (\neg p \to q)$ \begin{array}{c|c|c} p & q & p \to q & \neg p \to q& (p \to q) \land (\neg p \to q) \\ T & T & T&T &T \\ T & F & F&T &F\\ F & T & T& T &T\\ F & F & T& F&F\\ \end{array} e)$(p \leftrightarrow q) \lor (\neg p \leftrightarrow q)$ \begin{array}{c|c|c} p & q & p \leftrightarrow q &\neg p \leftrightarrow q& (p \leftrightarrow q) \lor (\neg p \leftrightarrow q) \\ T & T & T&F &T \\ T & F & F&T &T\\ F & T & F& T &T\\ F & F & T& F&T\\ \end{array} f)$(\neg p \leftrightarrow \neg q) \leftrightarrow ( p \leftrightarrow q)$ \begin{array}{c|c|c} p & q & \neg p \leftrightarrow \neg q &p \leftrightarrow q& (\neg p \leftrightarrow \neg q) \leftrightarrow ( p \leftrightarrow q) \\ T & T & T&T &T \\ T & F & F&F &T\\ F & T & F& F &T\\ F & F & T& T&T\\ \end{array}
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