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