Translate the following inference to logic notation: If Elisabeth were a musician, then Charles is playing tennis. For all x, if x_12 cooks, then x_12 is not a lawyer. For all x, x_12 is a lawyer. Charles is playing tennis if and only if Barbara is cooking. Therefore Elisabeth is not a musician.
p -> q. forall x: P(x) -> ~Q(x). forall x: Q(x). q <-> P(a). Therefore ~p.