Consider the following premises. If it is sunny, then it is late. It is sunny or William is a carpenter. If it is late, then James is drinking water. It is late or William is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: James is drinking water.
 From the fact that it is late or William is not a carpenter we can infer that if William were a carpenter, then it is late via rewriting. From the fact that if it is sunny, then it is late, that if William were a carpenter, then it is late, and that it is sunny or William is a carpenter we can infer that it is late via disjunction elimination. Finally, from the fact that if it is late, then James is drinking water, and that it is late we can infer that James is drinking water via modus ponens. Therefore, the answer is yes.