Consider the following premises. Karen is driving a car if and only if John is a mechanic. Karen is a writer. If Karen drives a car, then Karen is not a writer. John is a mechanic or Karen is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Karen is not writing a letter.
 From the fact that if Karen drives a car, then Karen is not a writer, and that Karen is a writer we can infer that Karen is not driving a car via modus tollens. From the fact that Karen is driving a car if and only if John is a mechanic, and that Karen is not driving a car we can infer that John is not a mechanic via biconditional elimination. Finally, from the fact that John is a mechanic or Karen is writing a letter, and that John is not a mechanic we can infer that Karen is writing a letter via disjunctive syllogism, which contradicts that Karen is not writing a letter. Therefore, the answer is no.