Translate the following inference to logic notation: For all x, x_5 is bored if and only if x_5 is happy. For all x, if x_5 takes a plane, then x_5 is bored. For all x, x_5 is not happy. For all x, if x_5 were bored, then x_5 is taking a plane. Therefore for all x, x_5 will not take a plane.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: ~Q(x). forall x: P(x) -> R(x). Therefore forall x: ~R(x).