Consider the following premises. For all x, x will not read a book. For all x, x will read a book if and only if x will play squash. There is at least one x for which if x reads a book, then x is playing squash. Can we infer the following from them? There is at least one x for which x will not play squash.
 From the fact that for all x, x will read a book if and only if x will play squash we can infer that for all x, if x plays squash, then x is reading a book. From the fact that there is at least one x for which if x reads a book, then x is playing squash, and that for all x, if x plays squash, then x is reading a book we can infer that there is at least one x for which x will read a book if and only if x will play squash. Finally, from the fact that there is at least one x for which x will read a book if and only if x will play squash, and that for all x, x will not read a book we can infer that there is at least one x for which x will not play squash. Therefore, the answer is yes.