Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11

Question:

The negation of $p ∧ (q → r)$ is
$¬ p ∧ (q ∧ r)$
$p ∨ (q ∨ r)$
$p ∨ (q ∨ r)$
$¬ p ∨ (q ∧ r)$

Step-by-Step Solution

Key Concept: The contrapositive of an implication is logically equivalent to the original statement.
Let $p$: my friends come, $q$: we go for picnic, $r$: weather will be fine. The statement is $p \rightarrow (q \wedge r)$. The contrapositive is $(\neg (q \wedge r)) \rightarrow \neg p$, which simplifies to $(\neg q \vee \neg r) \rightarrow \neg p$. This means: if my friends do not come or we do not go for picnic then weather will not be fine.
Correct Answer: F

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