Consider the following premises. If Mary writes a letter, then Charles is climbing a mountain. If Mary writes a letter, then Charles is climbing a mountain. If it is late, then Mary is writing a letter. If Charles climbs a mountain, then it is late. Can we infer the following from them? If is not true that Mary is writing a letter if and only if Charles is climbing a mountain.
 From the fact that if Charles climbs a mountain, then it is late, and that if it is late, then Mary is writing a letter we can infer that if Charles climbs a mountain, then Mary is writing a letter. Finally, from the fact that if Mary writes a letter, then Charles is climbing a mountain, and that if Charles climbs a mountain, then Mary is writing a letter we can infer that Mary is writing a letter if and only if Charles is climbing a mountain, which contradicts that If is not true that Mary is writing a letter if and only if Charles is climbing a mountain. Therefore, the answer is no.