Consider the following premises. Barbara is taking a plane if and only if it is sunny. It is overcast if and only if Elisabeth is playing a game. If John plays tennis, then Barbara is taking a plane. If it is sunny, then Elisabeth is playing a game. It is not overcast. If Barbara takes a plane, then John is playing tennis. Can we infer the following from them? John is not playing tennis.
 From the fact that it is overcast if and only if Elisabeth is playing a game, and that it is not overcast we can infer that Elisabeth is not playing a game. From the fact that if Barbara takes a plane, then John is playing tennis, and that if John plays tennis, then Barbara is taking a plane we can infer that Barbara is taking a plane if and only if John is playing tennis. From the fact that if it is sunny, then Elisabeth is playing a game, and that Elisabeth is not playing a game we can infer that it is not sunny. From the fact that Barbara is taking a plane if and only if it is sunny, and that it is not sunny we can infer that Barbara is not taking a plane. Finally, from the fact that Barbara is taking a plane if and only if John is playing tennis, and that Barbara is not taking a plane we can infer that John is not playing tennis. Therefore, the answer is yes.