Consider the following premises. It is overcast if and only if Patricia is cooking. John is an electrician if and only if Patricia is cooking. John is not an electrician. It is late if and only if it is overcast. Can we infer the following from them? It is not late.
 From the fact that John is an electrician if and only if Patricia is cooking, and that John is not an electrician we can infer that Patricia is not cooking. From the fact that it is overcast if and only if Patricia is cooking, and that Patricia is not cooking we can infer that it is not overcast. Finally, from the fact that it is late if and only if it is overcast, and that it is not overcast we can infer that it is not late. Therefore, the answer is yes.