Consider the following premises. It is overcast if and only if Linda is playing tennis. It is overcast or Joseph is running. Linda is not playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not running.
 From the fact that it is overcast if and only if Linda is playing tennis, and that Linda is not playing tennis we can infer that it is not overcast via biconditional elimination. Finally, from the fact that it is overcast or Joseph is running, and that it is not overcast we can infer that Joseph is running via disjunctive syllogism, which contradicts that Joseph is not running. Therefore, the answer is no.