Translate the following inference to logic notation: For all x, y will write a letter. For all x, y will listen to a song. For all x, if y writes a letter, then y is working. Therefore for all x, y will work and y will listen to a song.
forall x: P(x). forall x: Q(x). forall x: P(x) -> R(x). Therefore forall x: R(x) and Q(x).