To determine which of the given sets are examples of the null set (also known as the empty set), we will analyze each option step by step.
### Step-by-Step Solution:
1. **Set of odd numbers divisible by 2**:
- Odd numbers are: 1, 3, 5, 7, 9, ...
- No odd number can be divisible by 2.
- **Conclusion**: This set is a null set.
2. **Set of even prime numbers**:
- The only even prime number is 2.
- **Conclusion**: This set is not a null set as it contains the element {2}.
3. **Set A = {x : x in N, 1 < x ≤ 2}**:
- The natural numbers (N) are 1, 2, 3, ...
- The only number that satisfies 1 < x ≤ 2 is 2.
- **Conclusion**: This set is not a null set as it contains the element {2}.
4. **Set B = {x : x in N, 2x + 3 = 4}**:
- Solving for x:
- 2x + 3 = 4
- 2x = 1
- x = 1/2.
- Since 1/2 is not a natural number, there are no elements in this set.
- **Conclusion**: This set is a null set.
5. **Set C = {x : x is prime, 90 < x < 96}**:
- The integers between 90 and 96 are 91, 92, 93, 94, 95.
- None of these numbers are prime.
- **Conclusion**: This set is a null set.
6. **Set D = {x : x in N, x² + 1 = 0}**:
- The equation x² + 1 = 0 has no real solutions.
- Since there are no natural numbers that satisfy this equation, this set is empty.
- **Conclusion**: This set is a null set.
7. **Set E = {x : x in W, x + 3 ≤ 3}**:
- The whole numbers (W) are 0, 1, 2, 3, ...
- The inequality x + 3 ≤ 3 simplifies to x ≤ 0.
- The only whole number that satisfies this is 0.
- **Conclusion**: This set is not a null set as it contains the element {0}.
8. **Set F = {x : x in Q, 1 < x < 2}**:
- There are many rational numbers between 1 and 2 (e.g., 1.5, 1.75, etc.).
- **Conclusion**: This set is not a null set.
9. **Set G = {0}**:
- This set contains the element 0.
- **Conclusion**: This set is not a null set.
### Summary of Null Sets:
- The null sets from the options are:
- (i) Set of odd numbers divisible by 2
- (iv) Set B
- (v) Set C
- (vi) Set D
### Final Answer:
The examples of null sets are: (i), (iv), (v), and (vi).
