Consider the following premises. For all z_2, z_2 will not play tennis. Michael is a politician if and only if Patricia is an artist. Patricia is an artist if and only if James is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Michael is a politician.
 From the fact that for all z_2, z_2 will not play tennis we can infer that James is not playing tennis via universal instantiation. From the fact that Patricia is an artist if and only if James is playing tennis, and that James is not playing tennis we can infer that Patricia is not an artist via biconditional elimination. Finally, from the fact that Michael is a politician if and only if Patricia is an artist, and that Patricia is not an artist we can infer that Michael is not a politician via biconditional elimination, which contradicts that Michael is a politician. Therefore, the answer is no.