State which of the following sets are finite and which are infinite .
(i) {1,2,3,…….}
(ii) {1,2,3,……,999,1000}
(iii) Set of prime numbers less than 100 .
(iv) Set of concentric circles in a plane.

Answer

To determine whether the given sets are finite or infinite, we will analyze each set one by one.

### Step-by-Step Solution:

1. **Set (i): {1, 2, 3, ...}**
- This set includes all natural numbers starting from 1 and goes on indefinitely.
- Since there is no upper limit to the numbers in this set, it cannot be counted.
- **Conclusion:** This set is **infinite**.

2. **Set (ii): {1, 2, 3, ..., 999, 1000}**
- This set includes all natural numbers from 1 to 1000.
- Since the numbers are clearly defined and there is a specific upper limit (1000), we can count the elements in this set.
- **Conclusion:** This set is **finite**.

3. **Set (iii): Set of prime numbers less than 100**
- The prime numbers less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
- There are a finite number of prime numbers below 100, and we can list them all.
- **Conclusion:** This set is **finite**.

4. **Set (iv): Set of concentric circles in a plane**
- Concentric circles are circles that share the same center but have different radii.
- There is no limit to how many concentric circles can be drawn; we can keep adding circles with different radii indefinitely.
- **Conclusion:** This set is **infinite**.

### Final Summary:
- (i) Infinite
- (ii) Finite
- (iii) Finite
- (iv) Infinite