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: Evaluate the provided logical propositions.

Proposition 1: \( p \land q = F \) signifies that either \( p \) is False, or \( q \) is False, or both are False. 

Proposition 2: \( p \rightarrow q = F \) signifies that \( p \) must be True and \( q \) must be False. 

Step 2: Based on Proposition 2, given that \( p \rightarrow q \) evaluates to False, we establish: \[ p = T \quad \text{and} \quad q = F \] 

Conclusion: The determined truth values for \( p \) and \( q \) are True and False, respectively.