Consider the following premises. If it is sunny, then Thomas is reading a book. Thomas is reading a book if and only if Joseph is drinking water. If it is overcast, then Thomas is not reading a book. Joseph is drinking water or it is sunny. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that Thomas is reading a book if and only if Joseph is drinking water we can infer that if Joseph drinks water, then Thomas is reading a book via biconditional elimination. From the fact that if Joseph drinks water, then Thomas is reading a book, that if it is sunny, then Thomas is reading a book, and that Joseph is drinking water or it is sunny we can infer that Thomas is reading a book via disjunction elimination. Finally, from the fact that if it is overcast, then Thomas is not reading a book, and that Thomas is reading a book we can infer that it is not overcast via modus tollens. Therefore, the answer is yes.