p:x is an irrational number q:y is a transcendental number r:x is a rational number, if y is a transcendental number ⇒r:∼p↔q S1:r≡q∨p and S2:r≡∼(p↔∼q)
p
q
∼p
∼q
r ∼p↔q
Statement I q∨p
p↔∼q
Statement II ∼(p↔∼q)
T
T
F
F
F
T
F
T
T
F
F
T
T
T
T
F
F
T
T
F
T
T
T
F
F
F
T
T
F
F
F
T
It is clear from the table that r is not equivalent to either of the statements. Therefore, both statements are false. Hence, none of the given option is correct.