Translate the following inference to logic notation: For all x, x_3 will play tennis or x_3 will sleep. For all x, x_3 will sleep if and only if x_3 will cook. There is at least one x for which if x_3 plays tennis, then x_3 is cooking. Therefore there is at least one x for which x_3 will cook.
forall x: P(x) or Q(x). forall x: Q(x) <-> R(x). exists x: P(x) -> R(x). Therefore exists x: R(x).