Translate the following inference to logic notation: For all x, if y plays squash, then y is fast. There is at least one x for which y will play tennis or y will not climb a mountain. For all x, if y were fast, then y is climbing a mountain. Therefore there is at least one x for which if y plays squash, then y is playing tennis.
forall x: P(x) -> Q(x). exists x: R(x) or ~S(x). forall x: Q(x) -> S(x). Therefore exists x: P(x) -> R(x).