Consider the following premises. Jessica is an artist or it is late. Jessica is not an artist. For all z, z will cook. Can we infer the following from them? If we can, name the inference rule being used: Thomas is cooking or Elisabeth is a carpenter.
 From the fact that for all z, z will cook we can infer that Thomas is cooking via universal instantiation. From the fact that Jessica is an artist or it is late, and that Jessica is not an artist we can infer that it is late via disjunctive syllogism. From the fact that Thomas is cooking, and that it is late we can infer that Thomas is cooking and it is late via conjunction. From the fact that Thomas is cooking and it is late we can infer that Thomas is cooking via simplification. Finally, from the fact that Thomas is cooking we can infer that Thomas is cooking or Elisabeth is a carpenter via addition. Therefore, the answer is yes.