Consider the following premises. If Jennifer were a poet, then John is not a cashier. John is a cashier. Jennifer is a poet if and only if Joseph is a police officer. Joseph is a police officer. Can we infer the following from them? Joseph is playing a game.
 From the fact that if Jennifer were a poet, then John is not a cashier, and that John is a cashier we can infer that Jennifer is not a poet. From the fact that Jennifer is a poet if and only if Joseph is a police officer, and that Jennifer is not a poet we can infer that Joseph is not a police officer. From the fact that Joseph is not a police officer we can infer that Joseph is not a police officer or Joseph is playing a game. Finally, from the fact that Joseph is not a police officer or Joseph is playing a game, and that Joseph is a police officer we can infer that Joseph is playing a game. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.