Question

If \( p \land q \) is False and \( p \rightarrow q \) is False, then the truth values of \( p \) and \( q \) are:

• A. \( T, T \)
• B. \( T, F \)
• C. \( F, T \)
• D. \( F, F \)

Hint:

Remember that an implication \( p \rightarrow q \) is only False when \( p \) is True and \( q \) is False.

Answer 1

The Correct Option is B

Step 1: Analyze the given logical statements. 

Statement 1: \( p \land q = F \) implies that at least one of \( p \) or \( q \) is False. 

Statement 2: \( p \rightarrow q = F \) implies that \( p \) is True and \( q \) is False. 

Step 2: From Statement 2, since \( p \rightarrow q \) is False, we have: \[ p = T \quad \text{and} \quad q = F \] 

Conclusion: The truth values of \( p \) and \( q \) are \( T \) and \( F \), respectively.