Consider the following premises. If it snows, then it is raining. If Richard plays squash, then it is snowing. William is not writing a letter. If William writes a letter, then Richard is playing squash. William is a cashier if and only if Richard is playing squash. If it rains, then William is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: William is a cashier.
 From the fact that if it snows, then it is raining, and that if it rains, then William is writing a letter we can infer that if it snows, then William is writing a letter via transitivity. From the fact that if Richard plays squash, then it is snowing, and that if it snows, then William is writing a letter we can infer that if Richard plays squash, then William is writing a letter via transitivity. From the fact that if Richard plays squash, then William is writing a letter, and that if William writes a letter, then Richard is playing squash we can infer that Richard is playing squash if and only if William is writing a letter via biconditional introduction. From the fact that Richard is playing squash if and only if William is writing a letter, and that William is not writing a letter we can infer that Richard is not playing squash via biconditional elimination. Finally, from the fact that William is a cashier if and only if Richard is playing squash, and that Richard is not playing squash we can infer that William is not a cashier via biconditional elimination, which contradicts that William is a cashier. Therefore, the answer is no.