Translate the following inference to logic notation: For all x, x_7 is fast or x_7 is a taxi driver. For all x, x_7 will listen to a song or x_7 is not fast. There is at least one x for which x_7 is a taxi driver if and only if x_7 will listen to a song. Therefore there is at least one x for which x_7 will listen to a song.
forall x: P(x) or Q(x). forall x: R(x) or ~P(x). exists x: Q(x) <-> R(x). Therefore exists x: R(x).