Which of the following collection is not a set?

Options

A. The collection of all prime number between 10 and 30
B. The collection of all the mountains in india
C. The collection of all good people in world
D. The collection of all natural number.

Answer

To determine which of the following collections is not a set, we will analyze each option based on the definition of a set. A set is a well-defined collection of distinct objects, where the criteria for membership are clear and unambiguous.

**Step 1: Analyze the collection of all prime numbers between 10 and 30.**
- The prime numbers between 10 and 30 are: 11, 13, 17, 19, 23, and 29.
- This collection is well-defined and does not change from person to person.
- **Conclusion:** This is a set.

**Step 2: Analyze the collection of all mountains in India.**
- The mountains in India can be enumerated and are a fixed collection.
- This collection is also well-defined and does not change from person to person.
- **Conclusion:** This is a set.

**Step 3: Analyze the collection of all good people in the world.**
- The definition of "good people" is subjective and can vary from person to person.
- Different individuals may have different opinions about who qualifies as a "good person."
- **Conclusion:** This is not a set.

**Step 4: Analyze the collection of all natural numbers.**
- The natural numbers are well-defined and include numbers like 1, 2, 3, 4, and so on.
- This collection is fixed and does not change from person to person.
- **Conclusion:** This is a set.

**Final Conclusion:**
The collection that is not a set is the collection of all good people in the world.

---