Consider the following premises. Joseph is running. Joseph is happy. If it is late, then it is not sunny. If Joseph goes running, then Barbara is sleeping. If Barbara sleeps, then it is sunny. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that if Joseph goes running, then Barbara is sleeping, and that if Barbara sleeps, then it is sunny we can infer that if Joseph goes running, then it is sunny via transitivity. From the fact that if Joseph goes running, then it is sunny, and that Joseph is running we can infer that it is sunny via modus ponens. Finally, from the fact that if it is late, then it is not sunny, and that it is sunny we can infer that it is not late via modus tollens, which contradicts that It is late. Therefore, the answer is no.