Translate the following inference to logic notation: For all x, if x_7 makes tea, then x_7 is a scientist. For all x, x_7 will go running or x_7 will make tea. For all x, x_7 is a scientist if and only if x_7 will cook. For all x, if x_7 goes running, then x_7 is cooking. Therefore for all x, x_7 will cook.
forall x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: Q(x) <-> S(x). forall x: R(x) -> S(x). Therefore forall x: S(x).