Consider the following premises. Linda is sleeping. For all y, y is an electrician if and only if y will cook. If Barbara were an electrician, then Linda is not sleeping. Can we infer the following from them? Barbara is not cooking.
 From the fact that for all y, y is an electrician if and only if y will cook we can infer that Barbara is an electrician if and only if Barbara is cooking. From the fact that if Barbara were an electrician, then Linda is not sleeping, and that Linda is sleeping we can infer that Barbara is not an electrician. Finally, from the fact that Barbara is an electrician if and only if Barbara is cooking, and that Barbara is not an electrician we can infer that Barbara is not cooking. Therefore, the answer is yes.