Solution Found!
Explain, without using a truth table, is true when p ,q,
Chapter 1, Problem 40E(choose chapter or problem)
Explain, without using a truth table, why \((p \vee \neg q) \wedge\) \)(q \vee \neg r) \wedge(r \vee \neg p)\) is true when \(p, q\), and \(r\) have the same truth value and it is false otherwise.
Equation Transcription:
Text Transcription:
(p vee neg q) wedge (q vee neg r) wedge (r vee neg p)
p,q
r
Questions & Answers
QUESTION:
Explain, without using a truth table, why \((p \vee \neg q) \wedge\) \)(q \vee \neg r) \wedge(r \vee \neg p)\) is true when \(p, q\), and \(r\) have the same truth value and it is false otherwise.
Equation Transcription:
Text Transcription:
(p vee neg q) wedge (q vee neg r) wedge (r vee neg p)
p,q
r
ANSWER:
Solution:
Step 1:
In this problem we need to explain without using a truth table , is true when p,q and r have the same truth value and it is false otherwise.
Given: is true. When p , q, and r have the same truth value and it is false otherwise.
Conjunction : If p and q are statements , then the statement (read p and q) is true only when both p and q are true , and is false otherwise.
Disjunction: If p and q are statements , then the statement (read p or q) is true when at least one of the two statements is true , and is false when both are false.
Negation:Let P stand for a given statement.Thenrepresents the logical opposite of P. When P is true, then
is false and vice versa.