Consider the following premises. For all x, if x climbs a mountain, then x is a bartender. If Patricia were a bartender, then it is raining. If it rains, then Joseph is reading a book. Can we infer the following from them? If Patricia climbs a mountain, then Joseph is reading a book.
 From the fact that for all x, if x climbs a mountain, then x is a bartender we can infer that if Patricia climbs a mountain, then Patricia is a bartender. From the fact that if Patricia were a bartender, then it is raining, and that if it rains, then Joseph is reading a book we can infer that if Patricia were a bartender, then Joseph is reading a book. Finally, from the fact that if Patricia climbs a mountain, then Patricia is a bartender, and that if Patricia were a bartender, then Joseph is reading a book we can infer that if Patricia climbs a mountain, then Joseph is reading a book. Therefore, the answer is yes.