Consider the following premises. Barbara is not a cashier. If Mary were a musician, then Barbara is a cashier. Mary is a musician if and only if Barbara is a cashier. Can we infer the following from them? Mary is not a musician.
 From the fact that Mary is a musician if and only if Barbara is a cashier we can infer that if Barbara were a cashier, then Mary is a musician. From the fact that if Barbara were a cashier, then Mary is a musician, and that if Mary were a musician, then Barbara is a cashier we can infer that Barbara is a cashier if and only if Mary is a musician. Finally, from the fact that Barbara is a cashier if and only if Mary is a musician, and that Barbara is not a cashier we can infer that Mary is not a musician. Therefore, the answer is yes.