Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11

Question:

The logically equivalent proposition of $p ↔ q$ is
$(p ↔ q) ∨ (p ↔ q)
$(p → q) ∧ (q → p)$
$(p ∧ q) ∨ (q → p)$
$(p ∧ q) ≡ (q ∨ p)$

Step-by-Step Solution

Key Concept: A disjunction of three propositions can be expressed using material conditional and De Morgan's laws.
Let $p$: Suyash will come today, $q$: Shalini will be at his home, $r$: they will go to party. The statement translates to $p \vee q \vee r$. Using logical equivalence: $(\neg q \wedge \neg r) \rightarrow p \equiv (q \vee r) \vee p \equiv p \vee q \vee r$.
Correct Answer: T

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