Consider the following premises. It is overcast if and only if Joseph is sad. Joseph is not sad. It is snowing if and only if it is overcast. If Karen plays tennis, then it is snowing. Can we infer the following from them? If we can, name the inference rule being used: Karen is playing tennis.
 From the fact that it is overcast if and only if Joseph is sad, and that Joseph is not sad we can infer that it is not overcast via biconditional elimination. From the fact that it is snowing if and only if it is overcast, and that it is not overcast we can infer that it is not snowing via biconditional elimination. Finally, from the fact that if Karen plays tennis, then it is snowing, and that it is not snowing we can infer that Karen is not playing tennis via modus tollens, which contradicts that Karen is playing tennis. Therefore, the answer is no.