Explain, without using a truth table, is true when p ,q, and r have the same truth value and it is false otherwise.

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.

Step-2:

By using the above definitions :

If p , q, and r have the same truth value then , ,and are true. Since by disjunction definition .

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