Translate the following inference to logic notation: For all x, if x_1 plays tennis, then x_1 is an office clerk. For all x, if x_1 works, then x_1 is playing tennis. There is at least one x for which if x_1 were an office clerk, then x_1 is playing tennis. Therefore there is at least one x for which if x_1 works, then x_1 is an office clerk.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> P(x). Therefore exists x: R(x) -> Q(x).