Consider the following premises. If Linda goes running, then Barbara is a scientist. Charles is an electrician if and only if Joseph is writing a letter. Charles is not an electrician. Barbara is not a scientist. If Patricia plays a game, then Linda is running. Can we infer the following from them? If we can, name the inference rule being used: Joseph is writing a letter.
 From the fact that if Linda goes running, then Barbara is a scientist, and that Barbara is not a scientist we can infer that Linda is not running via modus tollens. From the fact that if Patricia plays a game, then Linda is running, and that Linda is not running we can infer that Patricia is not playing a game via modus tollens. Finally, from the fact that Charles is an electrician if and only if Joseph is writing a letter, and that Charles is not an electrician we can infer that Joseph is not writing a letter via biconditional elimination, which contradicts that Joseph is writing a letter. Therefore, the answer is no.