Consider the following premises. John is writing a letter if and only if Elisabeth is drinking water. If Linda were an artist, then Elisabeth is drinking water. If Elisabeth drinks water, then John is writing a letter. Can we infer the following from them? The fact that Linda were an artist does not imply that John is writing a letter.
 From the fact that John is writing a letter if and only if Elisabeth is drinking water we can infer that if John writes a letter, then Elisabeth is drinking water. From the fact that if Elisabeth drinks water, then John is writing a letter, and that if John writes a letter, then Elisabeth is drinking water we can infer that Elisabeth is drinking water if and only if John is writing a letter. From the fact that Elisabeth is drinking water if and only if John is writing a letter we can infer that if Elisabeth drinks water, then John is writing a letter. Finally, from the fact that if Linda were an artist, then Elisabeth is drinking water, and that if Elisabeth drinks water, then John is writing a letter we can infer that if Linda were an artist, then John is writing a letter, which contradicts that The fact that Linda were an artist does not imply that John is writing a letter. Therefore, the answer is no.