Consider the following premises. For all x_21, if x_21 plays a game, then x_21 is a musician. For all x_21, if x_21 were a mechanic, then x_21 is a musician. For all x_21, x_21 is a mechanic or x_21 will play a game. For all x_21, x_21 is a musician if and only if x_21 is a politician. Can we infer the following from them? Joseph is not a politician.
 From the fact that for all x_21, if x_21 were a mechanic, then x_21 is a musician, that for all x_21, if x_21 plays a game, then x_21 is a musician, and that for all x_21, x_21 is a mechanic or x_21 will play a game we can infer that for all x_21, x_21 is a musician. From the fact that for all x_21, x_21 is a musician if and only if x_21 is a politician we can infer that for all x_21, if x_21 were a musician, then x_21 is a politician. Finally, from the fact that for all x_21, if x_21 were a musician, then x_21 is a politician, and that for all x_21, x_21 is a musician we can infer that for all x_21, x_21 is a politician, which contradicts that Joseph is not a politician. Therefore, the answer is no.