Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11

Question:

If $p → (¬ p ∨ q)$ is false, then the truth values of $p$ and $q$ are respectively
F, T
F, F
T, T
T, F

Step-by-Step Solution

Key Concept: A conditional $A \to B$ is false only when $A$ is true and $B$ is false.
When $p \to (\neg p \vee q)$ is false, the antecedent $p$ must be true and the consequent $(\neg p \vee q)$ must be false. For $(\neg p \vee q)$ to be false, both $\neg p$ and $q$ must be false. Therefore $p$ is true and both $\neg p$ and $q$ are false, which means $p$ is true and $q$ is false.
Correct Answer: T

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