Translate the following inference to logic notation: For all x, x will not sleep. For all x, if x sleeps, then x is bored. For all x, if x were bored, then x is sleeping. Robert is taking a plane if and only if Richard is bored. Therefore Robert is not taking a plane.
forall x: ~P(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). p <-> Q(a). Therefore ~p.