Consider the following premises. Mary is fast if and only if it is cloudy. William is a janitor if and only if Mary is fast. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is cloudy does not imply that William is a janitor.
 From the fact that William is a janitor if and only if Mary is fast we can infer that if Mary were fast, then William is a janitor via biconditional elimination. From the fact that Mary is fast if and only if it is cloudy we can infer that if it is cloudy, then Mary is fast via biconditional elimination. Finally, from the fact that if it is cloudy, then Mary is fast, and that if Mary were fast, then William is a janitor we can infer that if it is cloudy, then William is a janitor via transitivity, which contradicts that The fact that it is cloudy does not imply that William is a janitor. Therefore, the answer is no.