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