Consider the following premises. If Joseph plays squash, then it is cloudy. James is playing a game or Joseph is playing squash. If Karen were an artist, then it is sunny. If it is cloudy, then Karen is an artist. If James plays a game, then Karen is an artist. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that if Joseph plays squash, then it is cloudy, and that if it is cloudy, then Karen is an artist we can infer that if Joseph plays squash, then Karen is an artist via transitivity. From the fact that if James plays a game, then Karen is an artist, that if Joseph plays squash, then Karen is an artist, and that James is playing a game or Joseph is playing squash we can infer that Karen is an artist via disjunction elimination. Finally, from the fact that if Karen were an artist, then it is sunny, and that Karen is an artist we can infer that it is sunny via modus ponens. Therefore, the answer is yes.