Question

If \( p \wedge q \) is F, \( p \to q \) is F, then the truth values of p and q are _______ respectively.

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

Hint:

For implication \( p \to q \) to be false, p must be true and q false; check conjunction conditions systematically.

Answer 1

The Correct Option is B

For \( p \wedge q \) to be false, at least one of p or q must be false. For \( p \to q \) (implication) to be false, p must be true and q must be false (since \( p \to q \equiv \neg p \vee q \), false only when p is T and q is F).
Check: If p = T, q = F:
- \( p \wedge q = T \wedge F = F \).
- \( p \to q = T \to F = F \).
Both conditions are satisfied. Other combinations (e.g., p = F, q = T or p = F, q = F) make \( p \to q \) true. Thus, p = T, q = F.