Translate the following inference to logic notation: For all x, if x_1 were a carpenter, then x_1 is a lawyer. There is at least one x for which x_1 is a carpenter or x_1 is a police officer. For all x, if x_1 were a lawyer, then x_1 is playing tennis. For all x, if x_1 were a police officer, then x_1 is playing tennis. Therefore there is at least one x for which x_1 will play tennis.
forall x: P(x) -> Q(x). exists x: P(x) or R(x). forall x: Q(x) -> S(x). forall x: R(x) -> S(x). Therefore exists x: S(x).