Consider the following premises. David is a carpenter or it is raining. If it rains, then Joseph is cooking. If David were a carpenter, then Jennifer is climbing a mountain. If Jennifer climbs a mountain, then Sarah is an electrician. If Sarah were an electrician, then Joseph is cooking. Can we infer the following from them? Joseph is not cooking.
 From the fact that if Jennifer climbs a mountain, then Sarah is an electrician, and that if Sarah were an electrician, then Joseph is cooking we can infer that if Jennifer climbs a mountain, then Joseph is cooking. From the fact that if David were a carpenter, then Jennifer is climbing a mountain, and that if Jennifer climbs a mountain, then Joseph is cooking we can infer that if David were a carpenter, then Joseph is cooking. Finally, from the fact that if David were a carpenter, then Joseph is cooking, that if it rains, then Joseph is cooking, and that David is a carpenter or it is raining we can infer that Joseph is cooking, which contradicts that Joseph is not cooking. Therefore, the answer is no.