Consider the following premises. Karen is a mechanic if and only if Richard is climbing a mountain. Karen is taking a plane if and only if Richard is not climbing a mountain. Karen is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Karen is not taking a plane.
 From the fact that Karen is a mechanic if and only if Richard is climbing a mountain, and that Karen is not a mechanic we can infer that Richard is not climbing a mountain via biconditional elimination. From the fact that Karen is taking a plane if and only if Richard is not climbing a mountain we can infer that if Richard doesn't climb a mountain, then Karen is taking a plane via biconditional elimination. Finally, from the fact that if Richard doesn't climb a mountain, then Karen is taking a plane, and that Richard is not climbing a mountain we can infer that Karen is taking a plane via modus ponens, which contradicts that Karen is not taking a plane. Therefore, the answer is no.