Translate the following inference to logic notation: For all x, if x_5 were a cashier, then x_5 is making tea. For all x, if x_5 takes a plane, then x_5 is making tea. For all x, x_5 will take a plane. There is at least one x for which if x_5 works, then x_5 is not making tea. Therefore there is at least one x for which x_5 will not work.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: R(x). exists x: S(x) -> ~Q(x). Therefore exists x: ~S(x).