Consider the following premises. Joseph is writing a letter if and only if it is snowing. If it is late, then Joseph is writing a letter. If Joseph writes a letter, then it is late. Can we infer the following from them? The fact that it is late does not imply that it is snowing.
 From the fact that if Joseph writes a letter, then it is late, and that if it is late, then Joseph is writing a letter we can infer that Joseph is writing a letter if and only if it is late. From the fact that Joseph is writing a letter if and only if it is snowing we can infer that if Joseph writes a letter, then it is snowing. From the fact that Joseph is writing a letter if and only if it is late we can infer that if it is late, then Joseph is writing a letter. Finally, from the fact that if it is late, then Joseph is writing a letter, and that if Joseph writes a letter, then it is snowing we can infer that if it is late, then it is snowing, which contradicts that The fact that it is late does not imply that it is snowing. Therefore, the answer is no.