Translate the following inference to logic notation: For all x, x will play tennis. For all x, x will cook if and only if x will play tennis. There is at least one x for which if x were a lawyer, then x is cooking. Therefore there is at least one x for which x will cook.
forall x: P(x). forall x: Q(x) <-> P(x). exists x: R(x) -> Q(x). Therefore exists x: Q(x).