Translate the following inference to logic notation: For all x, x_10 will not write a letter. There is at least one x for which x_10 is a server if and only if x_10 is a doctor. For all x, if x_10 were a doctor, then x_10 is a server. For all x, if x_10 were a doctor, then x_10 is writing a letter. Therefore there is at least one x for which x_10 is not a server.
forall x: ~P(x). exists x: Q(x) <-> R(x). forall x: R(x) -> Q(x). forall x: R(x) -> P(x). Therefore exists x: ~Q(x).