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?
the set containing the drama most watched by women and the drama least watched by men in the friday night line - up	○	○
the set containing only the show in the friday night line - up with the worst dressed actors	○	○
the set containing only the show in the friday night line - up with the worst cast	○	○
the set of the two least watched shows overall in the friday night line - up	○	○
the set of the last three shows to air according to the friday night schedule	○	○

Explanation:

A well-defined set has clear, objective criteria that let anyone determine exactly which elements belong to it.

1. The criteria (most watched drama by women, least watched drama by men) are objective and measurable from the study data, so the set is well-defined.
2. "Worst dressed actors" is a subjective judgment with no clear, universal standard, so the set is not well-defined.
3. "Worst cast" is a subjective opinion with no objective, consistent measure, so the set is not well-defined.
4. "Two least watched shows overall" is an objective ranking from the study, so the set is well-defined.
5. The Friday night schedule is fixed, so the last three shows to air are clearly identifiable, making the set well-defined.

Answer:

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