Consider the following premises. If William plays tennis, then it is cold. If Karen makes tea, then Joseph is a poet. If it is cold, then Karen is making tea. William is playing tennis or Joseph is not a poet. Can we infer the following from them? If we can, name the inference rule being used: Karen is making tea if and only if William is playing tennis.
 From the fact that William is playing tennis or Joseph is not a poet we can infer that if Joseph were a poet, then William is playing tennis via rewriting. From the fact that if William plays tennis, then it is cold, and that if it is cold, then Karen is making tea we can infer that if William plays tennis, then Karen is making tea via transitivity. From the fact that if Karen makes tea, then Joseph is a poet, and that if Joseph were a poet, then William is playing tennis we can infer that if Karen makes tea, then William is playing tennis via transitivity. Finally, from the fact that if Karen makes tea, then William is playing tennis, and that if William plays tennis, then Karen is making tea we can infer that Karen is making tea if and only if William is playing tennis via biconditional introduction. Therefore, the answer is yes.