$[10$ Pts$]$ Use logical reasoning to solve the following puzzil:

Five frimils go to the movies to watch ether Barhe or Oppentucimer. Bither Alice or Bob, or both, watch Barbie. Cindy and Don watch different momes. If Bllen watchics Barbic, then so does Cindy. Alice and Don watch the rame movie. If Bod matchios Barbic, then so do Alice and Elten. Who watches what movie? Define five besic propositions $A,B,C,D,E$ and use these to deseribe the five statetenents abone. Then use logical reasoning to derive tise truth of each of thowe busic propositions: heamer? Start by axuming that Bob watches Borbie and get a confrodichien That E arr true or falor