Consider the following premises. If Patricia writes a letter, then it is raining. Patricia is not a soldier. If it rains, then it is late. If it is late, then Patricia is writing a letter. Patricia is a soldier if and only if it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that Patricia is a soldier if and only if it is raining, and that Patricia is not a soldier we can infer that it is not raining via biconditional elimination. From the fact that if it is late, then Patricia is writing a letter, and that if Patricia writes a letter, then it is raining we can infer that if it is late, then it is raining via transitivity. From the fact that if it is late, then it is raining, and that if it rains, then it is late we can infer that it is late if and only if it is raining via biconditional introduction. Finally, from the fact that it is late if and only if it is raining, and that it is not raining we can infer that it is not late via biconditional elimination, which contradicts that It is late. Therefore, the answer is no.