To categorize the given elements into finite sets and infinite sets, let's understand the concept of finite and infinite sets first.
- A finite set has a countable number of elements.
- An infinite set has an uncountable number of elements that go on indefinitely.
### Given Elements:
1. Set of cities in Pakistan
2. 24
3. Set of universities in Lahore
4. Set of whole numbers
5. Set of negative integers
6. Set of points on a line segment
7. Set of vowels of the alphabet
8. Multan
Let's analyze and categorize each element:
#### Finite Sets:
1. Set of cities in Pakistan: The number of cities in Pakistan is countable.
2. Set of universities in Lahore: The number of universities in Lahore is countable.
3. Set of points on a line segment: This might seem infinite, but if we consider points defined directly only by the segment's endpoints (and optionally some intermediary points), it's finite.
4. Set of vowels of the alphabet: The vowels (A, E, I, O, U) are countable.
5. 24: This is a single number, so it's considered a singular finite element.
6. Multan: This is a single city name, so it's considered a singular finite element.
#### Infinite Sets:
1. Set of whole numbers: Whole numbers (0, 1, 2, 3, …) continue indefinitely.
2. Set of negative integers: Negative integers (…, -3, -2, -1) continue indefinitely.
### Categorization:
Finite Sets:
1. Set of cities in Pakistan
2. 24
3. Set of universities in Lahore
4. Set of points on a line segment
5. Set of vowels of the alphabet
6. Multan
Infinite Sets:
1. Set of whole numbers
2. Set of negative integers
The final categorization would be:
Finite Sets:
- Set of cities in Pakistan
- Set of universities in Lahore
- Set of points on a line segment
- Set of vowels of the alphabet
Infinite Sets:
- Set of whole numbers
- Set of negative integers
