Translate the following inference to logic notation: For all x, x_8 is a doctor if and only if x_8 will listen to a song. For all x, x_8 is a cashier or x_8 will listen to a song. For all x, x_8 is a doctor if and only if x_8 is a cashier. Therefore for all x, x_8 is a doctor.
forall x: P(x) <-> Q(x). forall x: R(x) or Q(x). forall x: P(x) <-> R(x). Therefore forall x: P(x).