Translate the following inference to logic notation: For all x, x_8 is a poet if and only if x_8 will listen to a song. For all x, x_8 will not listen to a song. For all x, x_8 is a poet or x_8 is fast. Therefore Barbara is fast.
forall x: P(x) <-> Q(x). forall x: ~Q(x). forall x: P(x) or R(x). Therefore R(a).