Let `A ={1,2,{3,4},5}`. Which of the following statements are incorrect and why ?
(i) `{3,4} subA`
(ii) `{3,4} in A`
(iii) `{{3,4}}sub A`
(iv) `1 in A`
(v) `1 sub A`
(vi) `{1,2,5} sub A`
(vii) `{1,2,5} in A`
(viii) `{1,2,3} sub A`
(ix) `phi in A`
(x) `phi sub A`
(xi) `{phi} sub A`.

Explanation

To determine which statements about the set \( A = \{1, 2, \{3, 4\}, 5\} \) are incorrect, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement (i)**: \(\{3, 4\} \subset A\)
- **Analysis**: The set \(\{3, 4\}\) is not a subset of \(A\) because neither 3 nor 4 is an element of \(A\). The only element in \(A\) that relates to \(\{3, 4\}\) is \(\{3, 4\}\) itself, which is an element of \(A\), not a subset.
- **Conclusion**: This statement is **incorrect**.

2. **Statement (ii)**: \(\{3, 4\} \in A\)
- **Analysis**: The set \(\{3, 4\}\) is indeed an element of \(A\).
- **Conclusion**: This statement is **correct**.

3. **Statement (iii)**: \(\{\{3, 4\}\} \subset A\)
- **Analysis**: The set \(\{\{3, 4\}\}\) is a subset of \(A\) because it contains the element \(\{3, 4\}\) which is present in \(A\).
- **Conclusion**: This statement is **correct**.

4. **Statement (iv)**: \(1 \in A\)
- **Analysis**: The number 1 is an element of \(A\).
- **Conclusion**: This statement is **correct**.

5. **Statement (v)**: \(1 \subset A\)
- **Analysis**: The number 1 is not a set, so it cannot be a subset of \(A\).
- **Conclusion**: This statement is **incorrect**.

6. **Statement (vi)**: \(\{1, 2, 5\} \subset A\)
- **Analysis**: The elements 1, 2, and 5 are all present in \(A\), so \(\{1, 2, 5\}\) is a subset of \(A\).
- **Conclusion**: This statement is **correct**.

7. **Statement (vii)**: \(\{1, 2, 5\} \in A\)
- **Analysis**: The set \(\{1, 2, 5\}\) is not an element of \(A\); \(A\) contains the individual elements 1, 2, and 5, but not the set \(\{1, 2, 5\}\).
- **Conclusion**: This statement is **incorrect**.

8. **Statement (viii)**: \(\{1, 2, 3\} \subset A\)
- **Analysis**: The element 3 is not in \(A\), so \(\{1, 2, 3\}\) cannot be a subset of \(A\).
- **Conclusion**: This statement is **incorrect**.

9. **Statement (ix)**: \(\emptyset \in A\)
- **Analysis**: The empty set \(\emptyset\) is not an element of \(A\).
- **Conclusion**: This statement is **incorrect**.

10. **Statement (x)**: \(\emptyset \subset A\)
- **Analysis**: The empty set is a subset of every set, including \(A\).
- **Conclusion**: This statement is **correct**.

11. **Statement (xi)**: \(\{\emptyset\} \subset A\)
- **Analysis**: The set \(\{\emptyset\}\) is not a subset of \(A\) because \(\emptyset\) is not an element of \(A\).
- **Conclusion**: This statement is **incorrect**.

### Summary of Incorrect Statements:
- (i) \(\{3, 4\} \subset A\) - Incorrect
- (v) \(1 \subset A\) - Incorrect
- (vii) \(\{1, 2, 5\} \in A\) - Incorrect
- (viii) \(\{1, 2, 3\} \subset A\) - Incorrect
- (ix) \(\emptyset \in A\) - Incorrect
- (xi) \(\{\emptyset\} \subset A\) - Incorrect