Translate the following inference to logic notation: For all x, y_1 is happy if and only if y_1 will make tea. There is at least one x for which if y_1 listens to a song, then y_1 is happy. For all x, if y_1 makes tea, then y_1 is listening to a song. Therefore there is at least one x for which if y_1 makes tea, then y_1 is listening to a song.
forall x: P(x) <-> Q(x). exists x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) -> R(x).