Consider the following premises. For all x_7, x_7 is a cashier if and only if x_7 is a carpenter. Thomas is not cooking. Barbara is a carpenter if and only if Thomas is cooking. Can we infer the following from them? Barbara is not a cashier.
 From the fact that for all x_7, x_7 is a cashier if and only if x_7 is a carpenter we can infer that Barbara is a cashier if and only if Barbara is a carpenter. From the fact that Barbara is a carpenter if and only if Thomas is cooking, and that Thomas is not cooking we can infer that Barbara is not a carpenter. Finally, from the fact that Barbara is a cashier if and only if Barbara is a carpenter, and that Barbara is not a carpenter we can infer that Barbara is not a cashier. Therefore, the answer is yes.