Consider the following premises. John is making tea or Elisabeth is not writing a letter. Richard is driving a car if and only if Susan is a soldier. If John makes tea, then Susan is a soldier. Can we infer the following from them? If Elisabeth writes a letter, then Richard is driving a car.
 From the fact that John is making tea or Elisabeth is not writing a letter we can infer that if Elisabeth writes a letter, then John is making tea. From the fact that Richard is driving a car if and only if Susan is a soldier we can infer that if Susan were a soldier, then Richard is driving a car. From the fact that if Elisabeth writes a letter, then John is making tea, and that if John makes tea, then Susan is a soldier we can infer that if Elisabeth writes a letter, then Susan is a soldier. Finally, from the fact that if Elisabeth writes a letter, then Susan is a soldier, and that if Susan were a soldier, then Richard is driving a car we can infer that if Elisabeth writes a letter, then Richard is driving a car. Therefore, the answer is yes.