Question:
What is the truth value of the proposition (P → Q) ∧ (¬Q) when P is true and Q is false?
What is the truth value of the proposition (P → Q) ∧ (¬Q) when P is true and Q is false?
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T implies F is false, and false AND anything is false.
Updated On: Jul 2, 2026
- True
- False
- Cannot be determined
- Not a valid formula
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The Correct Option is B
Solution and Explanation
Step 1: Substitute the values. With P true and Q false, evaluate \( P \rightarrow Q \). An implication is false only when the antecedent is true and the consequent is false, so \( T \rightarrow F = F \).
Step 2: Evaluate \( \neg Q \). Since Q is false, \( \neg Q = T \).
Step 3: Combine with AND: \[ (P \rightarrow Q) \wedge (\neg Q) = F \wedge T = F. \] The proposition is False.
Step 2: Evaluate \( \neg Q \). Since Q is false, \( \neg Q = T \).
Step 3: Combine with AND: \[ (P \rightarrow Q) \wedge (\neg Q) = F \wedge T = F. \] The proposition is False.
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