Translate the following inference to logic notation: For all x, if x_6 were a doctor, then x_6 is not an astronaut. For all x, x_6 will write a letter if and only if x_6 will work. For all x, x_6 is a doctor if and only if x_6 will write a letter. For all x, x_6 is an astronaut. Therefore for all x, x_6 will not work.
forall x: P(x) -> ~Q(x). forall x: R(x) <-> S(x). forall x: P(x) <-> R(x). forall x: Q(x). Therefore forall x: ~S(x).