To determine which of the following collections are sets, we need to apply the definition of a set: a set is a well-defined collection of distinct objects. Let's analyze each collection step by step.
### Step-by-Step Solution:
1. **Collection of odd natural numbers less than 50**:
- The odd natural numbers less than 50 are: 1, 3, 5, 7, ..., 49.
- This collection is well-defined and consists of distinct objects.
- **Conclusion**: This is a set.
2. **Collection of four colors of a rainbow**:
- A rainbow has seven colors: violet, indigo, blue, green, yellow, orange, red.
- Different people may choose different combinations of four colors, leading to ambiguity.
- **Conclusion**: This is not a set.
3. **Collection of first three days of a week**:
- The first three days of the week are: Sunday, Monday, Tuesday.
- This collection is well-defined and consists of distinct objects.
- **Conclusion**: This is a set.
4. **Collection of all tall students of your class**:
- The definition of "tall" can vary from person to person, leading to confusion.
- **Conclusion**: This is not a set.
5. **Collection of all clever students of your school**:
- Similar to the previous case, the definition of "clever" is subjective and varies.
- **Conclusion**: This is not a set.
6. **Collection of all rich people of Bengaluru**:
- The definition of "rich" is also subjective and can differ based on perspective.
- **Conclusion**: This is not a set.
7. **Collection of some multiples of 5**:
- The term "some" is vague; it does not specify how many multiples to include.
- **Conclusion**: This is not a set.
8. **Collection of all prime numbers**:
- Prime numbers are well-defined: they are natural numbers greater than 1 with exactly two distinct positive divisors (1 and the number itself).
- The collection includes: 2, 3, 5, 7, 11, ...
- **Conclusion**: This is a set.
9. **Collection of all even integers which lie between -5 and 15**:
- The even integers in this range are: -4, -2, 0, 2, 4, 6, 8, 10, 12, 14.
- This collection is well-defined and consists of distinct objects.
- **Conclusion**: This is a set.
10. **Collection of all good cricket players of India**:
- The definition of "good" can vary greatly among individuals.
- **Conclusion**: This is not a set.
11. **Collection of three youngest students of your class**:
- The ages of students can be compared to find the three youngest, making this collection well-defined.
- **Conclusion**: This is a set.
12. **Collection of three healthy students of your class**:
- The definition of "healthy" can differ from person to person, leading to ambiguity.
- **Conclusion**: This is not a set.
### Final Summary:
- **Sets**: (i), (iii), (viii), (ix), (xi)
- **Not Sets**: (ii), (iv), (v), (vi), (vii), (x), (xii)
