Translate the following inference to logic notation: For all x, if x_7 sleeps, then x_7 is a nurse. For all x, if x_7 writes a letter, then x_7 is sleeping. For all x, x_7 will cook or x_7 will write a letter. For all x, x_7 will cook if and only if x_7 is a nurse. Therefore for all x, x_7 is a nurse.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) or R(x). forall x: S(x) <-> Q(x). Therefore forall x: Q(x).