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