Consider the following premises. If Karen plays a game, then Sarah is writing a letter. If Linda were a poet, then Karen is playing a game. If Sarah writes a letter, then Linda is a poet. Karen is not playing a game. Can we infer the following from them? Sarah is not writing a letter.
 From the fact that if Sarah writes a letter, then Linda is a poet, and that if Linda were a poet, then Karen is playing a game we can infer that if Sarah writes a letter, then Karen is playing a game. From the fact that if Karen plays a game, then Sarah is writing a letter, and that if Sarah writes a letter, then Karen is playing a game we can infer that Karen is playing a game if and only if Sarah is writing a letter. Finally, from the fact that Karen is playing a game if and only if Sarah is writing a letter, and that Karen is not playing a game we can infer that Sarah is not writing a letter. Therefore, the answer is yes.