Consider the following premises. Joseph is playing squash or Sarah is taking a plane. If Joseph plays squash, then David is bored. If Sarah takes a plane, then David is bored. It is late or David is not bored. Can we infer the following from them? It is late.
 From the fact that if Joseph plays squash, then David is bored, that if Sarah takes a plane, then David is bored, and that Joseph is playing squash or Sarah is taking a plane we can infer that David is bored. From the fact that it is late or David is not bored we can infer that if David were bored, then it is late. Finally, from the fact that if David were bored, then it is late, and that David is bored we can infer that it is late. Therefore, the answer is yes.