Consider the following premises. For all x_10, if x_10 goes running, then x_10 is a cashier. For all x_10, x_10 will play tennis. For all x_10, x_10 is a cashier if and only if x_10 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a cashier or x_10 is a mechanic.
 From the fact that for all x_10, x_10 is a cashier if and only if x_10 will play tennis we can infer that for all x_10, if x_10 plays tennis, then x_10 is a cashier via universal biconditional elimination. From the fact that for all x_10, x_10 will play tennis we can infer that for all x_10, x_10 will play tennis or x_10 will go running via universal addition. From the fact that for all x_10, if x_10 plays tennis, then x_10 is a cashier, that for all x_10, if x_10 goes running, then x_10 is a cashier, and that for all x_10, x_10 will play tennis or x_10 will go running we can infer that for all x_10, x_10 is a cashier via universal disjunction elimination. Finally, from the fact that for all x_10, x_10 is a cashier we can infer that for all x_10, x_10 is a cashier or x_10 is a mechanic via universal addition. Therefore, the answer is yes.