Consider the following premises. Patricia is not a cashier. It is cold if and only if Mary is writing a letter. Michael is a soldier if and only if Patricia is a cashier. Mary is writing a letter if and only if Michael is a soldier. Can we infer the following from them? It is not cold or Patricia is a bartender.
 From the fact that Michael is a soldier if and only if Patricia is a cashier, and that Patricia is not a cashier we can infer that Michael is not a soldier. From the fact that Mary is writing a letter if and only if Michael is a soldier, and that Michael is not a soldier we can infer that Mary is not writing a letter. From the fact that it is cold if and only if Mary is writing a letter, and that Mary is not writing a letter we can infer that it is not cold. Finally, from the fact that it is not cold we can infer that it is not cold or Patricia is a bartender. Therefore, the answer is yes.