Translate the following inference to logic notation: For all x, if x_11 goes running, then x_11 is playing tennis. For all x, x_11 is a nurse. For all x, x_11 is a nurse if and only if x_11 will go running. Therefore for all x, x_11 will play tennis or x_11 is an office clerk.
forall x: P(x) -> Q(x). forall x: R(x). forall x: R(x) <-> P(x). Therefore forall x: Q(x) or S(x).