Consider the following premises. If it rains, then Michael is not a musician. It is raining or it is late. For all x, x is a musician. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that for all x, x is a musician we can infer that Michael is a musician via universal instantiation. From the fact that if it rains, then Michael is not a musician, and that Michael is a musician we can infer that it is not raining via modus tollens. Finally, from the fact that it is raining or it is late, and that it is not raining we can infer that it is late via disjunctive syllogism, which contradicts that It is not late. Therefore, the answer is no.