Translate the following inference to logic notation: For all x, y will play squash if and only if y will sleep. Richard is not a sailor. If Barbara sleeps, then Richard is a sailor. If Richard were a sailor, then Barbara is sleeping. Therefore Barbara is not playing squash.
forall x: P(x) <-> Q(x). ~p. Q(a) -> p. p -> Q(a). Therefore ~P(a).