Translate the following inference to logic notation: Jessica is not listening to a song. If Charles were a doctor, then Barbara is happy. Barbara is happy if and only if Jessica is a cashier. For all x, if x_15 were a cashier, then x_15 is listening to a song. Therefore Charles is not a doctor.
~P(a). p -> q. q <-> Q(a). forall x: Q(x) -> P(x). Therefore ~p.