Consider the following premises. It is sunny or it is late. David is reading a book. If it is sunny, then Elisabeth is writing a letter. If it is late, then it is overcast. If it is overcast, then Elisabeth is writing a letter. Can we infer the following from them? Elisabeth is writing a letter and David is reading a book.
 From the fact that if it is late, then it is overcast, and that if it is overcast, then Elisabeth is writing a letter we can infer that if it is late, then Elisabeth is writing a letter. From the fact that if it is sunny, then Elisabeth is writing a letter, that if it is late, then Elisabeth is writing a letter, and that it is sunny or it is late we can infer that Elisabeth is writing a letter. Finally, from the fact that Elisabeth is writing a letter, and that David is reading a book we can infer that Elisabeth is writing a letter and David is reading a book. Therefore, the answer is yes.