Translate the following inference to logic notation: For all x, if x_7 were a musician, then x_7 is cooking. For all x, if x_7 were a soldier, then x_7 is a musician. For all x, if x_7 plays tennis, then x_7 is a soldier. There is at least one x for which if x_7 cooks, then x_7 is playing tennis. Therefore there is at least one x for which if x_7 cooks, then x_7 is playing tennis.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) -> R(x). exists x: Q(x) -> S(x). Therefore exists x: Q(x) -> S(x).