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