Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11
Question:
If $p → (q ∨ r)$ is False, then the truth values of $p, q, r$ are respectively (where $T$ is True and $F$ is False)
T, F, F
F, T, T
F, F, F
T, T, F
Step-by-Step Solution
Key Concept: A biconditional $A \equiv B$ is true only when both sides have the same truth value.
Given $p \equiv (q \vee r)$: False, $p$: True, $q \vee r$: False. When $p$ is true and $(q \vee r)$ is false, the biconditional $p \equiv (q \vee r)$ is false. For $(q \vee r)$ to be false, both $q$ and $r$ must be false.
Correct Answer: F