Final answer:
Sets must have a clear and precise definition for membership. The collections of days that begin with 'T', girls in a school, and all odd numbers less than 30 meet these criteria and are sets. Other listed items involve subjective judgments, making them not sets.
Step-by-step explanation:
The question is asking which of the listed items are sets. A set is a collection of distinct objects, considered as an object in its own right. For a collection to be a set, it should be well-defined; the rule for membership of the set should be unambiguous. Here are the justifications for each item:
- (a) The collection of all the days in a week beginning with the letter 'T' is a set because it includes Tuesday and Thursday, which are precisely defined and recognizable.
- (b) The collection of all difficult questions in the chapter on sets is not a set because 'difficult' is subjective and cannot be precisely defined.
- (c) The collection of girls in your school is a set because it includes a specific group of individuals that can be identified and counted.
- (d) The collection of national emblems of Nepal is a set because it refers to a clearly defined group of symbols representing the country.
- (e) The collection of all active teachers in the school is a set, as it includes specific individuals who are currently teaching at the school.
- (f) The collection of all odd numbers less than 30 is a set because it is a clear mathematical definition that can be listed (1, 3, 5, 7, ... 29).
- (g) The collection of all beautiful flowers in the park is not a set because 'beautiful' is a subjective term and what is considered beautiful can vary from person to person.
Therefore, the correct answer is (c) (a), (c), (f), as these collections are well-defined and have clear membership criteria.