Question

In the following truth table, what does X stand for? 

 

• A. \( [P \wedge Q] \)
• B. \( [P \vee Q] \)
• C. \( [P \rightarrow Q] \)
• D. \( [P \leftrightarrow Q] \)

Hint:

The biconditional operation \( P \leftrightarrow Q \) is true when P and Q have the same truth value (either both true or both false).

Answer 1

The Correct Option is D

We are given the truth table for the variables P, Q, and X. To determine what X stands for, we need to analyze the values of X based on the conditions of P and Q.

By checking each row:
When P = 1 and Q = 1, X = 1.
When P = 1 and Q = 0, X = 0.
When P = 0 and Q = 1, X = 0.
When P = 0 and Q = 0, X = 1.

The truth values of X align with the biconditional logical operation \([P \leftrightarrow Q]\), which is true if P and Q have the same truth value (both true or both false). Thus, the correct operation for X is \([P \leftrightarrow Q]\).

Therefore, the correct option is:
\([P \leftrightarrow Q]\)