Let `A={phi,{phi},2,{2,phi},3},` which of the following are true ? `{:((i),phiinA,(i),phisubA,(iii),{phi}inA),((iv),{phi}subA,(v),2subA,(vi),{2","phi}subA),((vii),{{2}","{3}} subA,(viii),{2","3}!inA, (ix),{phi","2","3}subA.):}`

Answer

To solve the question regarding the set \( A = \{\phi, \{\phi\}, 2, \{2, \phi\}, 3\} \), we need to evaluate the truth of each statement provided. Let's analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement (i): \( \phi \in A \)**
- The empty set \( \phi \) is indeed an element of \( A \).
- **Conclusion**: True.

2. **Statement (ii): \( \phi \subset A \)**
- The empty set \( \phi \) is a subset of every set.
- **Conclusion**: True.

3. **Statement (iii): \( \{\phi\} \in A \)**
- The set \( \{\phi\} \) is explicitly listed as an element of \( A \).
- **Conclusion**: True.

4. **Statement (iv): \( \phi \subset A \)**
- As stated earlier, \( \phi \) is a subset of every set.
- **Conclusion**: True.

5. **Statement (v): \( 2 \subset A \)**
- The number \( 2 \) is an element of \( A \), but it is not a subset since it is not enclosed in brackets.
- **Conclusion**: False.

6. **Statement (vi): \( \{2, 5\} \subset A \)**
- The set \( \{2, 5\} \) is not a subset of \( A \) because \( 5 \) is not an element of \( A \).
- **Conclusion**: False.

7. **Statement (vii): \( \{2, 3\} \subset A \)**
- The set \( \{2, 3\} \) is not a subset of \( A \) because \( 2 \) is an element but not a set, and \( 3 \) is also an element but not enclosed in brackets.
- **Conclusion**: False.

8. **Statement (viii): \( \{2, 3\} \notin A \)**
- The set \( \{2, 3\} \) is not an element of \( A \) since neither \( 2 \) nor \( 3 \) is enclosed in brackets.
- **Conclusion**: True.

9. **Statement (ix): \( \{ \phi, 2, 3 \} \subset A \)**
- The set \( \{ \phi, 2, 3 \} \) is not a subset of \( A \) because \( 2 \) is not a set.
- **Conclusion**: False.

### Summary of Truth Values:
- (i) True
- (ii) True
- (iii) True
- (iv) True
- (v) False
- (vi) False
- (vii) False
- (viii) True
- (ix) False