Translate the following inference to logic notation: For all x, if x_5 writes a letter, then x_5 is cooking. For all x, x_5 will sleep. For all x, x_5 is a lawyer. For all x, if x_5 were a lawyer, then x_5 is cooking. Therefore for all x, x_5 will sleep and x_5 will cook.
forall x: P(x) -> Q(x). forall x: R(x). forall x: S(x). forall x: S(x) -> Q(x). Therefore forall x: R(x) and Q(x).