Question

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

• A. T, T
• B. T, F
• C. F, T
• D. F, F

Hint:

To solve logical expressions, check the truth tables of logical operators like AND (\(\land\)) and implication (\(\rightarrow\)).

Answer 1

The Correct Option is C

Step 1: Understanding the conditions. 
For \( p \land q = \text{F} \) and \( p \rightarrow q = \text{F} \), we know the following: - \( p \land q = \text{F} \) implies that at least one of \( p \) or \( q \) must be false. - \( p \rightarrow q = \text{F} \) implies that \( p \) is true and \( q \) is false.

Step 2: Conclusion. 
Thus, the only possible combination is \( p = \text{F} \) and \( q = \text{T} \).

Therefore, the correct answer is (C).