Translate the following inference to logic notation: There is at least one x for which if y_4 listens to a song, then y_4 is not climbing a mountain. For all x, y_4 will cook. For all x, y_4 will cook if and only if y_4 will climb a mountain. Therefore there is at least one x for which y_4 will not listen to a song.
exists x: P(x) -> ~Q(x). forall x: R(x). forall x: R(x) <-> Q(x). Therefore exists x: ~P(x).