Consider the following premises. Jennifer is working or Linda is sleeping. Jennifer is working if and only if Joseph is writing a letter. Joseph is writing a letter or Linda is not sleeping. Can we infer the following from them? Joseph is writing a letter.
 From the fact that Joseph is writing a letter or Linda is not sleeping we can infer that if Linda sleeps, then Joseph is writing a letter. From the fact that Jennifer is working if and only if Joseph is writing a letter we can infer that if Jennifer works, then Joseph is writing a letter. Finally, from the fact that if Jennifer works, then Joseph is writing a letter, that if Linda sleeps, then Joseph is writing a letter, and that Jennifer is working or Linda is sleeping we can infer that Joseph is writing a letter. Therefore, the answer is yes.