JEE Math Practice Question

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 $$ \sim \left( {p \leftrightarrow \sim q} \right)$$

1. A.Statement − 1 is false, Statement − 2 is false
2. B.Statement −1 is false, Statement −2 is true
3. C.Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
4. D.Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1