Translate the following inference to logic notation: For all x, if x_5 plays squash, then x_5 is cooking. For all x, x_5 will play squash and x_5 is a writer. There is at least one x for which if x_5 were a soldier, then x_5 is cooking. Therefore there is at least one x for which x_5 will cook.
forall x: P(x) -> Q(x). forall x: P(x) and R(x). exists x: S(x) -> Q(x). Therefore exists x: Q(x).