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Consider the two logical expressions: (p ∨ q) ∧ ¬p and ¬p ∧ q. Determine which of the following is correct: Statement-1: The two expressions are logically equivalent. Statement-2: The final columns of their truth tables match exactly.

1. Statement-1 is false, Statement-2 is true.
2. Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1.
3. Statement-1 is true, Statement-2 is true; Statement-2 does not correctly explain Statement-1.
4. Statement-1 is true, Statement-2 is false.

Correct answer: Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1.

Solution

Both logical expressions yield the same truth values under all possible interpretations of p and q, confirming their logical equivalence. Since the truth tables for both expressions match exactly, Statement-2 accurately supports Statement-1.

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