Which of the following are sets ? Justify your answer
(i) A team of eleven best cricket playes in the world.
(ii) The collection of difficult problems in a book.
(iii) The collection of all boys in the eleventh class of a particlular school.

Answer

To determine whether each collection is a set, we need to analyze the definitions and characteristics of the collections provided in the question.

### Step-by-Step Solution:

1. **Analyzing (i) A team of eleven best cricket players in the world:**
- The term "best" is subjective and can vary from person to person. Different people may have different opinions on who the best players are.
- Since the criteria for membership in this collection (who qualifies as "best") is not well-defined and can lead to ambiguity, this collection does not satisfy the definition of a set.

**Conclusion:** This is **not a set**.

2. **Analyzing (ii) The collection of difficult problems in a book:**
- Similar to the first case, the term "difficult" is also subjective. What one person finds difficult, another may not.
- Because the criteria for what constitutes a "difficult problem" can vary widely among individuals, this collection is also not well-defined.

**Conclusion:** This is **not a set**.

3. **Analyzing (iii) The collection of all boys in the eleventh class of a particular school:**
- This collection is well-defined. It specifies a particular group (all boys) within a specific context (the eleventh class of a particular school).
- Each element in this collection can be clearly identified and there is no ambiguity regarding who qualifies as a member of this set.

**Conclusion:** This is a **set**.

### Final Summary:
- (i) Not a set (due to subjective criteria)
- (ii) Not a set (due to subjective criteria)
- (iii) Set (due to well-defined criteria)