Consider the following premises. Joseph is drinking water. It is overcast. It is cold or it is raining. If Michael were an office clerk, then Joseph is not drinking water. Michael is an office clerk if and only if it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that if Michael were an office clerk, then Joseph is not drinking water, and that Joseph is drinking water we can infer that Michael is not an office clerk via modus tollens. From the fact that Michael is an office clerk if and only if it is cold, and that Michael is not an office clerk we can infer that it is not cold via biconditional elimination. Finally, from the fact that it is cold or it is raining, and that it is not cold we can infer that it is raining via disjunctive syllogism, which contradicts that It is not raining. Therefore, the answer is no.