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Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number” and r be the statement “x is a rational number iff y is a transcendental number”. Statement-1: r is equivalent to either q or p Statement-2: r is equivalent to ~(p ↔ ~q).

1. Statement-1 is false, Statement-2 is true
2. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
3. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
4. Statement-1 is true, Statement-2 is false

Correct answer: Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Solution

Statement-1 is true because the biconditional relationship in r implies that either x being irrational or y being transcendental must hold true. Statement-2 is also true as it correctly represents the logical equivalence of r, but it does not explain why Statement-1 is true since it does not directly relate to the disjunction of p or q.

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