Translate the following inference to logic notation: For all x, if x_2 goes running, then x_2 is sad. For all x, x_2 will go running or x_2 is not a sailor. For all x, if x_2 were sad, then x_2 is a sailor. Therefore for all x, x_2 is a sailor if and only if x_2 is sad.
forall x: P(x) -> Q(x). forall x: P(x) or ~R(x). forall x: Q(x) -> R(x). Therefore forall x: R(x) <-> Q(x).