Solved: In 47–50 (a) use the logical equivalences p q p q

Chapter 2, Problem 50E

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QUESTION:

In 47-50 (a) use the logical equivalences \(p \rightarrow q \equiv \sim p \vee q\) and \(p \leftrightarrow q \equiv(\sim p \vee q) \wedge(\sim q \vee p)\) to rewrite the given statement forms without using the symbol \(\rightarrow\) or \(\leftrightarrow\), and

(b) use the logical equivalence \(p \vee q \equiv \sim(\sim p \wedge \sim q)\) to rewrite each statement form using only \(\wedge\) and \(\sim\).

\((p \rightarrow(q \rightarrow r)) \leftrightarrow((p \wedge q) \rightarrow r)\)

Text Transcription:

p rightarrow q equiv sim p vee q

p leftrightarrow q equiv(sim p vee q) wedge(sim q vee p)

rightarrow

leftrightarrow

p vee q equiv sim(sim p wedge sim q)

wedge

sim

(p rightarrow(q rightarrow r)) leftrightarrow((p wedge q) rightarrow r)

Questions & Answers

QUESTION:

In 47-50 (a) use the logical equivalences \(p \rightarrow q \equiv \sim p \vee q\) and \(p \leftrightarrow q \equiv(\sim p \vee q) \wedge(\sim q \vee p)\) to rewrite the given statement forms without using the symbol \(\rightarrow\) or \(\leftrightarrow\), and

(b) use the logical equivalence \(p \vee q \equiv \sim(\sim p \wedge \sim q)\) to rewrite each statement form using only \(\wedge\) and \(\sim\).

\((p \rightarrow(q \rightarrow r)) \leftrightarrow((p \wedge q) \rightarrow r)\)

Text Transcription:

p rightarrow q equiv sim p vee q

p leftrightarrow q equiv(sim p vee q) wedge(sim q vee p)

rightarrow

leftrightarrow

p vee q equiv sim(sim p wedge sim q)

wedge

sim

(p rightarrow(q rightarrow r)) leftrightarrow((p wedge q) rightarrow r)

ANSWER:

Solution:Step 1: In this problem, we have to rewrite the given statement(a) use the logical equivalences p q p q and p q (p q) (q p) to rewrite the given statement forms without using the symbol or

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