Consider the following premises. For all y, if y were a mechanic, then y is reading a book. For all y, y is a cashier if and only if y is a scientist. There is at least one y for which if y were a scientist, then y is a mechanic. Can we infer the following from them? There is at least one y for which if y were a cashier, then y is reading a book.
 From the fact that for all y, y is a cashier if and only if y is a scientist we can infer that for all y, if y were a cashier, then y is a scientist. From the fact that for all y, if y were a cashier, then y is a scientist, and that there is at least one y for which if y were a scientist, then y is a mechanic we can infer that there is at least one y for which if y were a cashier, then y is a mechanic. Finally, from the fact that there is at least one y for which if y were a cashier, then y is a mechanic, and that for all y, if y were a mechanic, then y is reading a book we can infer that there is at least one y for which if y were a cashier, then y is reading a book. Therefore, the answer is yes.