Consider the following premises. If Joseph drinks water, then it is overcast. It is sunny or Joseph is drinking water. Patricia is playing tennis or it is not sunny. If Patricia plays tennis, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that Patricia is playing tennis or it is not sunny we can infer that if it is sunny, then Patricia is playing tennis via rewriting. From the fact that if it is sunny, then Patricia is playing tennis, and that if Patricia plays tennis, then it is overcast we can infer that if it is sunny, then it is overcast via transitivity. Finally, from the fact that if it is sunny, then it is overcast, that if Joseph drinks water, then it is overcast, and that it is sunny or Joseph is drinking water we can infer that it is overcast via disjunction elimination, which contradicts that It is not overcast. Therefore, the answer is no.