Translate the following inference to logic notation: For all x, if x_10 were a sailor, then x_10 is sleeping. For all x, x_10 is excited if and only if x_10 will sleep. For all x, x_10 is a sailor or x_10 is not excited. Therefore for all x, x_10 is a sailor if and only if x_10 is excited.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: P(x) or ~R(x). Therefore forall x: P(x) <-> R(x).