Solution Found!
Solved: In 47–50 (a) use the logical equivalences p ?q ??p
Chapter 2, Problem 49E(choose chapter or problem)
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 \(\sim\).
\((p \rightarrow r) \leftrightarrow(q \rightarrow r)\)
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 r) leftrightarrow(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 \(\sim\).
\((p \rightarrow r) \leftrightarrow(q \rightarrow r)\)
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 r) leftrightarrow(q rightarrow r)
ANSWER:Solution:
Step 1:
In this problem, we have to rewrite the given statement
We have to 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 ↔