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.