Consider the following premises. If Joseph writes a letter, then it is snowing. It is cloudy if and only if it is snowing. If Patricia were an artist, then Joseph is writing a letter. Can we infer the following from them? If Patricia were an artist, then it is cloudy.
 From the fact that it is cloudy if and only if it is snowing we can infer that if it snows, then it is cloudy. From the fact that if Patricia were an artist, then Joseph is writing a letter, and that if Joseph writes a letter, then it is snowing we can infer that if Patricia were an artist, then it is snowing. Finally, from the fact that if Patricia were an artist, then it is snowing, and that if it snows, then it is cloudy we can infer that if Patricia were an artist, then it is cloudy. Therefore, the answer is yes.