Translate the following inference to logic notation: For all x, if x_13 makes tea, then x_13 is a carpenter. For all x, x_10 will not cook. If William makes tea, then Barbara is cooking. For all x, if x_13 were a carpenter, then x_13 is making tea. Therefore William is not a carpenter.
forall x: P(x) -> Q(x). forall x: ~R(x). P(a) -> R(b). forall x: Q(x) -> P(x). Therefore ~Q(a).