3. (11 points) Let the sets Director, D, be a set of movie directors, Movie, M, be a set of movies, and Actor, A, be a set of actors. We define the following relations Page 1 of 3 CS2311 - Spring 2019 HW 4 Due: Fri. 02/17/19 appearedIn C Actor Movie or appeared!n C A M. where a appearedIn m if a was an actor who appeared in movie m . directedFilmDirector Movie or directedFilmD M. where - - d directedFilm m if d was the director of movie m . starredIn-Actor Movie of starredIn-A M, where a starredIn m if a was an actor with top 3 billing in movie m Express the following using only set operations and relations: (a) There must be actors who have both appeared in and starred in a movie. (b) Some people appear in movies they direct. (c) Some movies are directed by people who do not star in them Take the following relations and express what they mean in English. Think about what sets define the elements the relations is made up of (d) appearedIn o appearedIn-1 Is this relation (i) reflexive? (ii) symmetric? and (iii) transitive? (e) directedFilm o starredIn Is this relation (i) reflexive? (ii) symmetric? and (iii) transitive? 3. (11 points) Let the sets Director, D, be a set of movie directors, Movie, M, be a set of movies, and Actor, A, be a set of actors. We define the following relations Page 1 of 3 CS2311 - Spring 2019 HW 4 Due: Fri. 02/17/19 appearedIn C Actor Movie or appeared!n C A M. where a appearedIn m if a was an actor who appeared in movie m . directedFilmDirector Movie or directedFilmD M. where - - d directedFilm m if d was the director of movie m . starredIn-Actor Movie of starredIn-A M, where a starredIn m if a was an actor with top 3 billing in movie m Express the following using only set operations and relations: (a) There must be actors who have both appeared in and starred in a movie. (b) Some people appear in movies they direct. (c) Some movies are directed by people who do not star in them Take the following relations and express what they mean in English. Think about what sets define the elements the relations is made up of (d) appearedIn o appearedIn-1 Is this relation (i) reflexive? (ii) symmetric? and (iii) transitive? (e) directedFilm o starredIn Is this relation (i) reflexive? (ii) symmetric? and (iii) transitive