(A) $\exists x \left( S(x) \land \forall y (P(y) \implies A(x,y) )\right)$
$\equiv \exists x \forall y \left( S(x) \land ( P(y) \implies A(x,y)) \right)$
Similarly,
(B) $\exists y \forall x \left( P(y) \land ( S(x) \implies A(y,x)) \right)$
(C) $\exists y \forall x \left( P(y) \land ( S(x) \implies A(x,y)) \right)$
(D) $\exists x \forall y \left( S(x) \land ( P(y) \implies A(y,x)) \right)$