Consider the following premises. If Joseph makes tea, then it is cold. If Barbara reads a book, then it is cold. If Sarah writes a letter, then Joseph is making tea. Barbara is reading a book or Sarah is writing a letter. Can we infer the following from them? It is cold.
 From the fact that if Sarah writes a letter, then Joseph is making tea, and that if Joseph makes tea, then it is cold we can infer that if Sarah writes a letter, then it is cold. Finally, from the fact that if Barbara reads a book, then it is cold, that if Sarah writes a letter, then it is cold, and that Barbara is reading a book or Sarah is writing a letter we can infer that it is cold. Therefore, the answer is yes.