Translate the following inference to logic notation: For all x, if x_3 sleeps, then x_3 is climbing a mountain. For all x, x_3 will climb a mountain if and only if x_3 will sleep. For all x, x_3 will not sleep. Therefore for all x, x_3 will not climb a mountain.
forall x: P(x) -> Q(x). forall x: Q(x) <-> P(x). forall x: ~P(x). Therefore forall x: ~Q(x).