Translate the following inference to logic notation: It is overcast if and only if James is a nurse. James is listening to a song or it is overcast. For all x, x_12 will listen to a song if and only if x_12 is a nurse. Therefore James is a nurse.
p <-> P(a). Q(a) or p. forall x: Q(x) <-> P(x). Therefore P(a).