Let A= {{1,2,3},{4,5} , {6,7,8,9}} .
(i) {1,2,3} `subA`
(ii) {{4,5}} `subA`.

Answer

To determine whether the given sets are subsets of set A, we need to analyze the elements of set A and the proposed subsets.

Given:
\[ A = \{ \{1, 2, 3\}, \{4, 5\}, \{6, 7, 8, 9\} \} \]

### (i) Check if \(\{1, 2, 3\} \subset A\)

1. **Identify the elements of set A**:
- The elements of set A are \(\{1, 2, 3\}\), \(\{4, 5\}\), and \(\{6, 7, 8, 9\}\).

2. **Determine if \(\{1, 2, 3\}\) is an element of A**:
- We see that \(\{1, 2, 3\}\) is indeed one of the elements in set A.

3. **Conclusion**:
- Since \(\{1, 2, 3\}\) is an element of A, it is not a subset of A. A subset must consist of elements that are contained within the set, not just be an element of it.

### (ii) Check if \(\{\{4, 5\}\} \subset A\)

1. **Identify the elements of set A**:
- Again, the elements of set A are \(\{1, 2, 3\}\), \(\{4, 5\}\), and \(\{6, 7, 8, 9\}\).

2. **Determine if \(\{\{4, 5\}\}\) is a subset of A**:
- The set \(\{\{4, 5\}\}\) contains one element, which is \(\{4, 5\}\).
- Since \(\{4, 5\}\) is an element of A, it means that \(\{\{4, 5\}\}\) is a subset of A.

3. **Conclusion**:
- Therefore, \(\{\{4, 5\}\}\) is indeed a subset of A.

### Final Answers:
- (i) \(\{1, 2, 3\} \not\subset A\)
- (ii) \(\{\{4, 5\}\} \subset A\)