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