Translate the following inference to logic notation: For all x, y_1 is a bartender if and only if y_1 will work. If Karen works, then Karen is a musician. For all x, if y_1 were a musician, then y_1 is a bartender. Therefore Karen is a musician if and only if Karen is working.
forall x: P(x) <-> Q(x). Q(a) -> R(a). forall x: R(x) -> P(x). Therefore R(a) <-> Q(a).