Consider the following premises. Elisabeth is a sailor or Patricia is listening to a song. James is a cashier or Patricia is not listening to a song. If James were a cashier, then it is overcast. Michael is working if and only if Elisabeth is a sailor. If it is overcast, then Michael is working. Can we infer the following from them? Michael is working.
 From the fact that James is a cashier or Patricia is not listening to a song we can infer that if Patricia listens to a song, then James is a cashier. From the fact that if Patricia listens to a song, then James is a cashier, and that if James were a cashier, then it is overcast we can infer that if Patricia listens to a song, then it is overcast. From the fact that if Patricia listens to a song, then it is overcast, and that if it is overcast, then Michael is working we can infer that if Patricia listens to a song, then Michael is working. From the fact that Michael is working if and only if Elisabeth is a sailor we can infer that if Elisabeth were a sailor, then Michael is working. Finally, from the fact that if Elisabeth were a sailor, then Michael is working, that if Patricia listens to a song, then Michael is working, and that Elisabeth is a sailor or Patricia is listening to a song we can infer that Michael is working. Therefore, the answer is yes.