Let `A={phi,{phi},2,{2,phi,5}}`. Which of the following are true or false Justify your answer.
(i) `phi inA`
(ii) `{phi}inA`
(iii) `{2}inA`
(iv) `{5,phi}subA`
(v) `5subA`
(vi) `{5,{2}}notinA`
(vii) `{{5},{2}}notinA`
(viii) `{phi,(phi},(2,phi}}subA`
(ix) `{{phi}}subA`.

Answer

To solve the question, we will analyze each statement regarding the set \( A = \{\phi, \{\phi\}, 2, \{2, \phi, 5\}\} \) and determine whether they are true or false, providing justification for each.

### Step-by-Step Solution:

1. **Statement (i): \( \phi \in A \)**
- **Justification**: The symbol \( \phi \) (the empty set) is one of the elements of set \( A \).
- **Conclusion**: True.

2. **Statement (ii): \( \{\phi\} \in A \)**
- **Justification**: The set \( \{\phi\} \) is explicitly listed as one of the elements of set \( A \).
- **Conclusion**: True.

3. **Statement (iii): \( \{2\} \in A \)**
- **Justification**: The set \( \{2\} \) is not an element of \( A \); \( A \) contains the number 2, but not as a set.
- **Conclusion**: False.

4. **Statement (iv): \( \{5, \phi\} \subset A \)**
- **Justification**: The set \( \{5, \phi\} \) is not a subset of \( A \) because 5 is not an element of \( A \).
- **Conclusion**: False.

5. **Statement (v): \( 5 \subset A \)**
- **Justification**: The number 5 is not an element of \( A \), and thus cannot be a subset.
- **Conclusion**: False.

6. **Statement (vi): \( \{5, \{2\}\} \notin A \)**
- **Justification**: The set \( \{5, \{2\}\} \) is not an element of \( A \) since neither 5 nor \( \{2\} \) is in \( A \).
- **Conclusion**: True.

7. **Statement (vii): \( \{\{5\}, \{2\}\} \notin A \)**
- **Justification**: The set \( \{\{5\}, \{2\}\} \) is not an element of \( A \) because neither \( \{5\} \) nor \( \{2\} \) is in \( A \).
- **Conclusion**: True.

8. **Statement (viii): \( \{\phi, \{\phi\}, \{2, \phi\}\} \subset A \)**
- **Justification**: The set \( \{\phi, \{\phi\}, \{2, \phi\}\} \) is not a subset of \( A \) because \( \{2, \phi\} \) is not an element of \( A \).
- **Conclusion**: False.

9. **Statement (ix): \( \{\{\phi\}\} \subset A \)**
- **Justification**: The set \( \{\{\phi\}\} \) is a subset of \( A \) because \( \{\phi\} \) is an element of \( A \).
- **Conclusion**: True.

### Final Answers:
- (i) True
- (ii) True
- (iii) False
- (iv) False
- (v) False
- (vi) True
- (vii) True
- (viii) False
- (ix) True