Consider the following premises. John is driving a car or it is overcast. If John drives a car, then Linda is cooking. Linda is cooking or it is not overcast. If Linda cooks, then Patricia is a poet. Can we infer the following from them? Patricia is not a poet.
 From the fact that Linda is cooking or it is not overcast we can infer that if it is overcast, then Linda is cooking. From the fact that if John drives a car, then Linda is cooking, that if it is overcast, then Linda is cooking, and that John is driving a car or it is overcast we can infer that Linda is cooking. Finally, from the fact that if Linda cooks, then Patricia is a poet, and that Linda is cooking we can infer that Patricia is a poet, which contradicts that Patricia is not a poet. Therefore, the answer is no.