Consider the following premises. Robert is not writing a letter. John is driving a car if and only if it is sunny. If it is sunny, then Elisabeth is taking a plane. If Elisabeth takes a plane, then Robert is writing a letter. Can we infer the following from them? John is not driving a car.
 From the fact that if it is sunny, then Elisabeth is taking a plane, and that if Elisabeth takes a plane, then Robert is writing a letter we can infer that if it is sunny, then Robert is writing a letter. From the fact that if it is sunny, then Robert is writing a letter, and that Robert is not writing a letter we can infer that it is not sunny. Finally, from the fact that John is driving a car if and only if it is sunny, and that it is not sunny we can infer that John is not driving a car. Therefore, the answer is yes.