Translate the following inference to logic notation: For all x, x_3 will not climb a mountain. There is at least one x for which x_3 is a carpenter if and only if x_3 will cook. For all x, x_3 will climb a mountain if and only if x_3 is a carpenter. Therefore there is at least one x for which x_3 will not cook.
forall x: ~P(x). exists x: Q(x) <-> R(x). forall x: P(x) <-> Q(x). Therefore exists x: ~R(x).