Translate the following inference to logic notation: For all x, z will cook if and only if z will play tennis. There is at least one x for which z will not play tennis. For all x, if z were curious, then z is cooking. For all x, if z cooks, then z is curious. Therefore there is at least one x for which z is not curious.
forall x: P(x) <-> Q(x). exists x: ~Q(x). forall x: R(x) -> P(x). forall x: P(x) -> R(x). Therefore exists x: ~R(x).