Consider the following premises. If Jessica takes a plane, then Mary is climbing a mountain. It is cloudy if and only if Jessica is taking a plane. If Mary climbs a mountain, then it is cloudy. Can we infer the following from them? If is not true that Jessica is taking a plane if and only if it is cloudy.
 From the fact that it is cloudy if and only if Jessica is taking a plane we can infer that if it is cloudy, then Jessica is taking a plane. From the fact that if Jessica takes a plane, then Mary is climbing a mountain, and that if Mary climbs a mountain, then it is cloudy we can infer that if Jessica takes a plane, then it is cloudy. Finally, from the fact that if Jessica takes a plane, then it is cloudy, and that if it is cloudy, then Jessica is taking a plane we can infer that Jessica is taking a plane if and only if it is cloudy, which contradicts that If is not true that Jessica is taking a plane if and only if it is cloudy. Therefore, the answer is no.