Consider the following premises. If Thomas were a taxi driver, then Susan is playing tennis. If Susan plays tennis, then Karen is writing a letter. If Karen writes a letter, then Susan is playing tennis. Karen is not writing a letter. Susan is playing tennis if and only if Thomas is a taxi driver. Can we infer the following from them? Thomas is not a taxi driver.
 From the fact that if Susan plays tennis, then Karen is writing a letter, and that if Karen writes a letter, then Susan is playing tennis we can infer that Susan is playing tennis if and only if Karen is writing a letter. From the fact that Susan is playing tennis if and only if Thomas is a taxi driver we can infer that if Susan plays tennis, then Thomas is a taxi driver. From the fact that if Susan plays tennis, then Thomas is a taxi driver, and that if Thomas were a taxi driver, then Susan is playing tennis we can infer that Susan is playing tennis if and only if Thomas is a taxi driver. From the fact that Susan is playing tennis if and only if Karen is writing a letter, and that Karen is not writing a letter we can infer that Susan is not playing tennis. Finally, from the fact that Susan is playing tennis if and only if Thomas is a taxi driver, and that Susan is not playing tennis we can infer that Thomas is not a taxi driver. Therefore, the answer is yes.