Which of the following sets in an finite/infinite set ?
`(i)` Set of divisors of `24`
`(ii)` Set of all real number which lie between `1` and `2`
(iii) Set of all three digit natural numbers

Answer

Let's analyze each part of the question step by step to determine whether each set is finite or infinite.

### Step 1: Set of Divisors of 24
- **Identify the divisors of 24**: The divisors of 24 are the numbers that can divide 24 without leaving a remainder. These are:
- 1, 2, 3, 4, 6, 8, 12, 24
- **Count the divisors**: There are a total of 8 divisors.
- **Conclusion**: Since we can count the divisors, the set of divisors of 24 is a **finite set**.

### Step 2: Set of All Real Numbers Between 1 and 2
- **Identify the numbers between 1 and 2**: The set includes all rational and irrational numbers that lie between 1 and 2.
- **Count the numbers**: There are infinitely many numbers (for example, 1.1, 1.01, 1.001, etc.) that can be found between 1 and 2.
- **Conclusion**: Since we cannot count the numbers in this interval, the set of all real numbers between 1 and 2 is an **infinite set**.

### Step 3: Set of All Three-Digit Natural Numbers
- **Identify the range of three-digit natural numbers**: The three-digit natural numbers range from 100 to 999.
- **Count the numbers**: The total number of three-digit natural numbers can be calculated as:
- 999 - 100 + 1 = 900
- **Conclusion**: Since we can count the three-digit natural numbers, the set of all three-digit natural numbers is a **finite set**.

### Final Summary
- (i) Set of divisors of 24: **Finite set**
- (ii) Set of all real numbers between 1 and 2: **Infinite set**
- (iii) Set of all three-digit natural numbers: **Finite set**

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