Which of the following collections is a set 

1. easy examples in a book

2. tall trees in a campus

3. letters of word "beautiful"

4. divides of 30 less than 25

give proper reason

To determine whether a collection is a set, we need to check if it is **well-defined**. A collection is well-defined if there is a clear rule that allows us to decide whether an object belongs to the collection or not. In other words, for a set, we should be able to unambiguously determine its elements.

Let's analyze each collection:

1. **Easy examples in a book**

   - **Reasoning**: The term "easy examples" is subjective and can vary from person to person. What one person considers "easy" might not be the same for another person. Therefore, this collection is **not well-defined**.
   - **Conclusion**: **Not a set**.

2. **Tall trees in a campus**

   - **Reasoning**: The term "tall" is also subjective. Different people may have different interpretations of what qualifies as "tall." Thus, there is no clear rule to determine if a tree is included.
   - **Conclusion**: **Not a set**.

3. **Letters of the word "beautiful"**

   - **Reasoning**: The letters of the word "beautiful" are clearly defined and do not change based on individual interpretation. We can list the letters as {b, e, a, u, t, i, f, l}. Even though some letters repeat in the word, a set includes each unique element only once.
   - **Conclusion**: **This is a set**. 

4. **Divisors of 30 less than 25**

   - **Reasoning**: Divisors of 30 are numbers that divide 30 without leaving a remainder. They can be clearly listed: {1, 2, 3, 5, 6, 10, 15, 30}. The divisors less than 25 are {1, 2, 3, 5, 6, 10, 15}. Since we have a clear rule and a finite list, this collection is well-defined.
   - **Conclusion**: **This is a set**.

**Summary:**

- Collection 1: Not a set
- Collection 2: Not a set
- Collection 3: Is a set
- Collection 4: Is a set

Would you like more details or have any questions?

### Additional Questions:

1. What is the difference between a set and a non-set collection?
2. How do you determine if a set is finite or infinite?
3. Can a set have repeated elements, or must all elements be unique?
4. What are some examples of well-defined and not well-defined collections?
5. How does the definition of a set apply to mathematical operations like union and intersection?

**Tip:** When defining a set, ensure that the criteria for membership are objective and unambiguous.

Explore the concept of sets in mathematics with clear examples and definitions. Learn how to distinguish between sets and non-sets using well-defined criteria. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation