Translate the following inference to logic notation: For all x, z will climb a mountain if and only if z is sad. There is at least one x for which z will sleep if and only if z will work. For all x, z will work if and only if z will climb a mountain. For all x, z will not sleep. Therefore there is at least one x for which z is not sad.
forall x: P(x) <-> Q(x). exists x: R(x) <-> S(x). forall x: S(x) <-> P(x). forall x: ~R(x). Therefore exists x: ~Q(x).