1. (∃x)[Px • (∀y)(Py ⊃ y=x) • (∃y)(Qy • Rxy)]
2. (∃x)[Px • Sx • (∀y)∼Ryx]
-Which of the following propositions is derivable from the given premises in F?
A) (∃x)(∀y)~Rxy
B) (∃x)(Sx • Qx)
C) (∃x)(∃y)(Rxy • ∼Ryx)
D) (∀x)(Sx ⊃ Rxx)
E) (∀x)(Px ⊃ Rxx)

Question

Quizplus · Accepted Answer

C) is derivable because from the first premise, there exists an x related to some y by Rxy, and from the second premise, for any y, it is not the case that Ryx, which together imply the existence of an x and a y such that Rxy and not Ryx, satisfying the conditions for C.

1 (∃X)[Px • (∀Y)(Py ⊃ Y=x) • (∃Y)(Qy • Rxy)]