Question

on friday nights, a television network airs four sitcoms and three dramas on a fixed schedule. these seven shows are the network’s “friday night line - up.” the network conducted a study that determined how many people watch these shows among three groups: women, men, and overall. for each group, the seven shows were identified as either a drama or sitcom and ordered from most watched to least watched. based on this information, determine if each set is well - defined.
set | is the set well - defined?
| yes | no
the set containing only the show in the friday night line - up with the worst cast | |
the set containing the drama most watched by women and the drama least watched by men in the friday night line - up | |
the set of the last three shows to air according to the friday night schedule | |
the set containing only the show in the friday night line - up with the worst dressed actors | |
the set of the two least watched shows overall in the friday night line - up | |

Explanation:

A well-defined set has clear, objective criteria to determine membership.

1. For "the show with the worst cast": "Worst cast" is subjective (no universal standard), so membership is unclear.
2. For "most watched drama by women + least watched drama by men": The study provides ordered viewership data for these groups, so we can objectively identify these two shows.
3. For "last three shows in Friday schedule": The schedule is fixed, so we can objectively identify these shows.
4. For "show with worst dressed actors": "Worst dressed" is subjective (no universal standard), so membership is unclear.
5. For "two least watched shows overall": The study provides overall ordered viewership data, so we can objectively identify these two shows.

Answer:

1. The set containing only the show in the Friday night line-up with the worst cast: No
2. The set containing the drama most watched by women and the drama least watched by men in the Friday night line-up: Yes
3. The set of the last three shows to air according to the Friday night schedule: Yes
4. The set containing only the show in the Friday night line-up with the worst dressed actors: No
5. The set of the two least watched shows overall in the Friday night line-up: Yes