Translate the following inference to logic notation: There is at least one x for which y will sleep if and only if y will climb a mountain. For all x, y will play squash if and only if y will sleep. Therefore there is at least one x for which if y plays squash, then y is climbing a mountain.
exists x: P(x) <-> Q(x). forall x: R(x) <-> P(x). Therefore exists x: R(x) -> Q(x).