Question

If \[ p \rightarrow \left( \sim p \vee q \right) \text{ is false, then the truth values of } p \text{ and } q \text{ are respectively} \]

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

Hint:

For logical implications, the only way the implication is false is if the antecedent is true and the consequent is false.

Answer 1

The Correct Option is D

Step 1: Understanding the logical implication.
For the implication \( p \rightarrow (\sim p \vee q) \) to be false, the antecedent \( p \) must be true and the consequent \( (\sim p \vee q) \) must be false. Therefore, \( p = T \) and \( \sim p \vee q = F \). The only way \( \sim p \vee q \) can be false is if \( p = T \) and \( q = F \).

Step 2: Conclusion.
Thus, the truth values of \( p \) and \( q \) are \( T \) and \( F \), which makes option (D) the correct answer.