Consider the following premises. It is late or Elisabeth is not playing tennis. Thomas is sleeping if and only if Elisabeth is playing tennis. It is late if and only if Thomas is sleeping. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Thomas is sleeping if and only if it is late.
 From the fact that Thomas is sleeping if and only if Elisabeth is playing tennis we can infer that if Thomas sleeps, then Elisabeth is playing tennis via biconditional elimination. From the fact that it is late if and only if Thomas is sleeping we can infer that if it is late, then Thomas is sleeping via biconditional elimination. From the fact that it is late or Elisabeth is not playing tennis we can infer that if Elisabeth plays tennis, then it is late via rewriting. From the fact that if Thomas sleeps, then Elisabeth is playing tennis, and that if Elisabeth plays tennis, then it is late we can infer that if Thomas sleeps, then it is late via transitivity. Finally, from the fact that if Thomas sleeps, then it is late, and that if it is late, then Thomas is sleeping we can infer that Thomas is sleeping if and only if it is late via biconditional introduction, which contradicts that If is not true that Thomas is sleeping if and only if it is late. Therefore, the answer is no.