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