Consider the following premises. It is cloudy if and only if Jessica is cooking. If it is cloudy, then Patricia is an electrician. If Patricia were an electrician, then Jessica is cooking. Can we infer the following from them? If is not true that Jessica is cooking if and only if Patricia is an electrician.
 From the fact that it is cloudy if and only if Jessica is cooking we can infer that if Jessica cooks, then it is cloudy. From the fact that if Jessica cooks, then it is cloudy, and that if it is cloudy, then Patricia is an electrician we can infer that if Jessica cooks, then Patricia is an electrician. Finally, from the fact that if Jessica cooks, then Patricia is an electrician, and that if Patricia were an electrician, then Jessica is cooking we can infer that Jessica is cooking if and only if Patricia is an electrician, which contradicts that If is not true that Jessica is cooking if and only if Patricia is an electrician. Therefore, the answer is no.