Translate the following inference to logic notation: For all x, if x_5 works, then x_5 is a nurse. For all x, x_5 will work and x_5 will write a letter. For all x, if x_5 takes a plane, then x_5 is a nurse. Therefore for all x, x_5 is a nurse.
forall x: P(x) -> Q(x). forall x: P(x) and R(x). forall x: S(x) -> Q(x). Therefore forall x: Q(x).