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