Consider the following premises. For all x, if x drinks water, then x is playing squash. There is at least one x for which x will not write a letter. For all x, if x plays squash, then x is writing a letter. For all x, if x cooks, then x is drinking water. For all x, if x writes a letter, then x is playing squash. Can we infer the following from them? There is at least one x for which x will not cook.
 From the fact that for all x, if x cooks, then x is drinking water, and that for all x, if x drinks water, then x is playing squash we can infer that for all x, if x cooks, then x is playing squash. From the fact that for all x, if x plays squash, then x is writing a letter, and that for all x, if x writes a letter, then x is playing squash we can infer that for all x, x will play squash if and only if x will write a letter. From the fact that for all x, x will play squash if and only if x will write a letter, and that there is at least one x for which x will not write a letter we can infer that there is at least one x for which x will not play squash. Finally, from the fact that for all x, if x cooks, then x is playing squash, and that there is at least one x for which x will not play squash we can infer that there is at least one x for which x will not cook. Therefore, the answer is yes.