Translate the following inference to logic notation: For all x, x_6 will listen to a song or x_6 will not write a letter. There is at least one x for which if x_6 works, then x_6 is listening to a song. For all x, x_6 is not curious or x_6 will write a letter. For all x, x_6 is curious or x_6 will work. Therefore there is at least one x for which x_6 will listen to a song.
forall x: P(x) or ~Q(x). exists x: R(x) -> P(x). forall x: ~S(x) or Q(x). forall x: S(x) or R(x). Therefore exists x: P(x).