Consider the following premises. If it rains, then Susan is playing tennis. It is raining if and only if Charles is a carpenter. It is raining or Susan is not playing tennis. Can we infer the following from them? If we can, name the inference rule being used: The fact that Charles were a carpenter does not imply that Susan is playing tennis.
 From the fact that it is raining or Susan is not playing tennis we can infer that if Susan plays tennis, then it is raining via rewriting. From the fact that it is raining if and only if Charles is a carpenter we can infer that if Charles were a carpenter, then it is raining via biconditional elimination. From the fact that if it rains, then Susan is playing tennis, and that if Susan plays tennis, then it is raining we can infer that it is raining if and only if Susan is playing tennis via biconditional introduction. From the fact that it is raining if and only if Susan is playing tennis we can infer that if it rains, then Susan is playing tennis via biconditional elimination. Finally, from the fact that if Charles were a carpenter, then it is raining, and that if it rains, then Susan is playing tennis we can infer that if Charles were a carpenter, then Susan is playing tennis via transitivity, which contradicts that The fact that Charles were a carpenter does not imply that Susan is playing tennis. Therefore, the answer is no.