Consider the following premises. David is an office clerk if and only if Barbara is playing tennis. For all y, y will not drive a car. For all y, if y were an office clerk, then y is driving a car. For all y, if y drives a car, then y is an office clerk. Can we infer the following from them? Barbara is playing tennis.
 From the fact that for all y, if y drives a car, then y is an office clerk, and that for all y, if y were an office clerk, then y is driving a car we can infer that for all y, y will drive a car if and only if y is an office clerk. From the fact that for all y, y will drive a car if and only if y is an office clerk, and that for all y, y will not drive a car we can infer that for all y, y is not an office clerk. From the fact that for all y, y is not an office clerk we can infer that David is not an office clerk. Finally, from the fact that David is an office clerk if and only if Barbara is playing tennis, and that David is not an office clerk we can infer that Barbara is not playing tennis, which contradicts that Barbara is playing tennis. Therefore, the answer is no.