Translate the following inference to logic notation: For all x, x_1 will not sleep. For all x, x_1 will write a letter if and only if x_1 is a carpenter. For all x, if x_1 were a carpenter, then x_1 is sleeping. Therefore for all x, x_1 will not write a letter.
forall x: ~P(x). forall x: Q(x) <-> R(x). forall x: R(x) -> P(x). Therefore forall x: ~Q(x).