Consider the following premises. Elisabeth is playing tennis if and only if it is late. It is cold if and only if it is late. It is windy if and only if it is cloudy. It is windy if and only if it is cold. 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 Elisabeth is playing tennis if and only if it is late, and that Elisabeth is not playing tennis we can infer that it is not late via biconditional elimination. From the fact that it is cold if and only if it is late, and that it is not late we can infer that it is not cold via biconditional elimination. From the fact that it is windy if and only if it is cold, and that it is not cold we can infer that it is not windy via biconditional elimination. Finally, from the fact that it is windy if and only if it is cloudy, and that it is not windy we can infer that it is not cloudy via biconditional elimination, which contradicts that It is cloudy. Therefore, the answer is no.