Consider the following premises. If Karen were a musician, then Susan is excited. If Susan were excited, then Karen is a musician. John is not playing squash. Susan is excited if and only if John is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Karen is not a musician.
 From the fact that if Susan were excited, then Karen is a musician, and that if Karen were a musician, then Susan is excited we can infer that Susan is excited if and only if Karen is a musician via biconditional introduction. From the fact that Susan is excited if and only if Karen is a musician we can infer that if Karen were a musician, then Susan is excited via biconditional elimination. From the fact that Susan is excited if and only if John is playing squash, and that John is not playing squash we can infer that Susan is not excited via biconditional elimination. Finally, from the fact that if Karen were a musician, then Susan is excited, and that Susan is not excited we can infer that Karen is not a musician via modus tollens. Therefore, the answer is yes.