Translate the following inference to logic notation: There is at least one x for which x_12 is a nurse if and only if x_12 will make tea. For all x, x_12 will make tea or x_12 will not drink water. For all x, if x_12 were a nurse, then x_12 is a carpenter. Therefore there is at least one x for which if x_12 drinks water, then x_12 is a carpenter.
exists x: P(x) <-> Q(x). forall x: Q(x) or ~R(x). forall x: P(x) -> S(x). Therefore exists x: R(x) -> S(x).