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