State whether each of the following statement is true or false , Justify your answer .
(i) {2,3,4,5} and {3,6} are disjoint sets .
(ii) {a,e,I,ou} and {a,b,cd} are disjoint sets.
(iii) {2,6,10,14} and {3,7,11,15} are disjoint sets.
(iv) {2,6,10,14} and {3,7,11} are disjoint sets.

Answer

To determine whether each of the following statements is true or false, we need to check if the sets mentioned in each statement have any elements in common. If they do not share any elements, they are considered disjoint sets.

Let's analyze each statement step by step:

### (i) {2, 3, 4, 5} and {3, 6}

1. **Identify the elements in both sets**:
- Set A: {2, 3, 4, 5}
- Set B: {3, 6}

2. **Find the intersection of the two sets**:
- The common element is 3.

3. **Conclusion**:
- Since there is a common element (3), the sets are **not disjoint**.
- Therefore, the statement is **False**.

### (ii) {a, e, i, o, u} and {a, b, c, d}

1. **Identify the elements in both sets**:
- Set A: {a, e, i, o, u}
- Set B: {a, b, c, d}

2. **Find the intersection of the two sets**:
- The common element is a.

3. **Conclusion**:
- Since there is a common element (a), the sets are **not disjoint**.
- Therefore, the statement is **False**.

### (iii) {2, 6, 10, 14} and {3, 7, 11, 15}

1. **Identify the elements in both sets**:
- Set A: {2, 6, 10, 14}
- Set B: {3, 7, 11, 15}

2. **Find the intersection of the two sets**:
- There are no common elements.

3. **Conclusion**:
- Since there are no common elements, the sets are **disjoint**.
- Therefore, the statement is **True**.

### (iv) {2, 6, 10, 14} and {3, 7, 11}

1. **Identify the elements in both sets**:
- Set A: {2, 6, 10, 14}
- Set B: {3, 7, 11}

2. **Find the intersection of the two sets**:
- There are no common elements.

3. **Conclusion**:
- Since there are no common elements, the sets are **disjoint**.
- Therefore, the statement is **True**.

### Summary of Answers:
- (i) False
- (ii) False
- (iii) True
- (iv) True