Translate the following inference to logic notation: For all x, if x_1 were happy, then x_1 is listening to a song. For all x, x_1 is a poet. There is at least one x for which if x_1 were a poet, then x_1 is happy. Therefore there is at least one x for which x_1 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x). exists x: R(x) -> P(x). Therefore exists x: Q(x).