Translate the following inference to logic notation: For all x, x will work or x will listen to a song. For all x, x will not cook. There is at least one x for which x will cook or x is a politician. For all x, x will not work. Therefore some politicians will listen to a song.
forall x: P(x) or Q(x). forall x: ~R(x). exists x: R(x) or S(x). forall x: ~P(x). Therefore exists x: S(x) and Q(x).