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”. \[\] S1 : r is equivalent to either q or p \[\] S2 : r is equivalent to $ ^{\sim}(p \leftrightarrow \: ^{\sim}q)$

Question

$\begin {array} {1 1} \text{(A) S1 is true, S2 is false} \\ \text{(B) S1 is false,S2 is true} \\ \text{(C) both S1 and S2 are true} \\ \text{(D) both S1 and S2 are false} \end {array}$