Explain, without using a truth table, why (p ∨¬q) ∧ (q ∨¬r) ∧ (r ∨¬p) is true when p, q, and r have the same truth value and it is false otherwise.

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.