Consider the following premises. If William were a carpenter, then it is raining. If it rains, then it is sunny. If it is sunny, then David is playing tennis. If David plays tennis, then William is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is sunny if and only if William is a carpenter.
 From the fact that if it is sunny, then David is playing tennis, and that if David plays tennis, then William is a carpenter we can infer that if it is sunny, then William is a carpenter via transitivity. From the fact that if William were a carpenter, then it is raining, and that if it rains, then it is sunny we can infer that if William were a carpenter, then it is sunny via transitivity. Finally, from the fact that if it is sunny, then William is a carpenter, and that if William were a carpenter, then it is sunny we can infer that it is sunny if and only if William is a carpenter via biconditional introduction, which contradicts that If is not true that it is sunny if and only if William is a carpenter. Therefore, the answer is no.