Question

one hundred riders from several countries participated in a bicycle race. only eighty riders, including ravi and josh, finished the race. ravi finished 5th and josh was the winner. all the riders countries of origin and finishing times were recorded on the race register. no two riders who finished had the same time and those who did not finish were recorded as dnf. based on this information, determine if each set is well - defined.

set	is the set well - defined?
the set of riders who finished 10 minutes or less after the winner	○	○
the set of the three most tired riders at the end	○	○
the set of riders who started but did not finish the race	○	○
the set of riders with the best looking uniforms	○	○
the set of countries of origin of the first ten riders to finish	○	○

Explanation:

• A set is well-defined if there is an objective, clear criterion to determine membership.

1. Finishing time relative to the winner is a recorded, objective measure, so membership is clear.
2. "Most tired" is subjective with no objective measurement, so membership cannot be definitively determined.
3. Riders who did not finish are clearly marked as DNF, creating an objective criterion for membership.
4. "Best looking uniforms" is a subjective judgment with no universal standard, so membership is not clear.
5. The first ten finishers are a definite group, and their countries of origin are recorded, making membership objective.

Answer:

1. The set of riders who finished 10 minutes or less after the winner: Yes
2. The set of the three most tired riders at the end: No
3. The set of riders who started but did not finish the race: Yes
4. The set of riders with the best looking uniforms: No
5. The set of countries of origin of the first ten riders to finish: Yes