Translate the following inference to logic notation: Karen is playing a game if and only if Richard is taking a plane. If Richard cooks, then Richard is taking a plane. For all x, if x_4 listens to a song, then x_4 is cooking. For all x, if x_4 takes a plane, then x_4 is listening to a song. Karen is not playing a game. Therefore Richard is not cooking.
p <-> P(a). Q(a) -> P(a). forall x: R(x) -> Q(x). forall x: P(x) -> R(x). ~p. Therefore ~Q(a).