Translate the following inference to logic notation: For all x, x_12 will listen to a song if and only if x_12 will sleep. There is at least one x for which x_12 is a poet. For all x, x_12 will sleep and x_12 is a nurse. Therefore there is at least one x for which x_12 is a poet and x_12 will listen to a song.
forall x: P(x) <-> Q(x). exists x: R(x). forall x: Q(x) and S(x). Therefore exists x: R(x) and P(x).