Translate the following inference to logic notation: Sarah is working if and only if William is sleeping. For all x, x_11 will play tennis. For all x, if x_11 makes tea, then x_11 is not playing tennis. For all x, x_11 will work if and only if x_11 will make tea. Therefore William is not sleeping.
P(a) <-> p. forall x: Q(x). forall x: R(x) -> ~Q(x). forall x: P(x) <-> R(x). Therefore ~p.