Which of the following is a well-defined set? Justify your answer.

a. A collection of all boys in your class.

b. A collection of efficient doctors in Black Lion Hospital.

c. A collection of all natural numbers less than 100.

d. The collection of songs by Artist Tilahun Gessese

A well-defined set is one in which it is possible to determine with certainty whether any given object belongs to the set or not. Let's analyze each of the given options:

**a. A collection of all boys in your class.**  
- **Justification:** This is a well-defined set because you can clearly identify who is in your class and determine whether any given individual is a boy or not. The membership criteria are clear and unambiguous.

**b. A collection of efficient doctors in Black Lion Hospital.**  
- **Justification:** This is **not** a well-defined set because the term "efficient" is subjective and can vary depending on personal opinions or criteria. Different people may have different standards for what makes a doctor "efficient," making it difficult to determine the exact members of the set.

**c. A collection of all natural numbers less than 100.**  
- **Justification:** This is a well-defined set because the criteria are precise and mathematical. The set includes exactly the natural numbers from 1 to 99, and there is no ambiguity about whether a particular number is in the set.

**d. The collection of songs by Artist Tilahun Gessese.**  
- **Justification:** This is a well-defined set because the songs by Tilahun Gessese are a specific and identifiable group. You can clearly determine whether a particular song is by this artist, making it possible to establish the set with certainty.

**Summary:** Sets (a), (c), and (d) are well-defined, while set (b) is not.

Would you like more details on this or any other related questions?

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Here are 8 related questions for further practice:

1. What makes a set well-defined?
2. Can you give an example of a well-defined set that involves subjective criteria?
3. If a set is not well-defined, what are the potential issues that might arise?
4. How would you describe the set of all prime numbers less than 50?
5. Is the collection of all popular movies from 2020 a well-defined set? Why or why not?
6. Can the set of all tall people in a school be considered well-defined?
7. How would you define a set of all even integers using set-builder notation?
8. Is the set of all books written by Shakespeare well-defined? Why?

**Tip:** In mathematics, clarity and precision are crucial. When defining a set, ensure that the criteria for membership are objective and unambiguous.

Explore the concept of well-defined sets in mathematics with detailed examples and analysis. Understand the criteria for a set to be well-defined and apply it to different scenarios. Learn why sets like collections of natural numbers under 100 and songs by Tilahun Gessese qualify as well-defined sets.

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