Translate the following inference to logic notation: There is at least one x for which if x_6 were a nurse, then x_6 is a soldier. For all x, if x_6 works, then x_6 is a nurse. For all x, x_6 will play tennis if and only if x_6 will work. Therefore there is at least one x for which if x_6 plays tennis, then x_6 is a soldier.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) <-> R(x). Therefore exists x: S(x) -> Q(x).