If A and B are any two sets and U , the universal set , then correct match of the following is :
`{:("Column -I",,"Column -II"),((i) AuuA,,(a)U),((ii)AUU,,(b)A),((iii)AuuB,,(c)phi),((iv)Acapphi,,(d)BuuA.):}`

Answer

To solve the problem of matching the items in Column I with those in Column II, we will analyze each item in Column I and determine its corresponding match in Column II.

### Step-by-Step Solution:

1. **Match (i) A ∪ A**:
- The union of a set with itself is the set itself. Therefore, \( A \cup A = A \).
- **Match**: (i) A ∪ A corresponds to (b) A.

2. **Match (ii) A ∪ U**:
- The union of any set A with the universal set U is the universal set itself. Thus, \( A \cup U = U \).
- **Match**: (ii) A ∪ U corresponds to (a) U.

3. **Match (iii) A ∪ B**:
- The union of two sets A and B is the set that contains all elements from both A and B. This can also be expressed as \( A \cup B = B \cup A \).
- **Match**: (iii) A ∪ B corresponds to (d) B ∪ A.

4. **Match (iv) A ∩ φ**:
- The intersection of any set A with the empty set (φ) is the empty set itself, as there are no common elements. Thus, \( A \cap φ = φ \).
- **Match**: (iv) A ∩ φ corresponds to (c) φ.

### Final Matches:
- (i) A ∪ A → (b) A
- (ii) A ∪ U → (a) U
- (iii) A ∪ B → (d) B ∪ A
- (iv) A ∩ φ → (c) φ

### Summary of Matches:
1. (i) → (b)
2. (ii) → (a)
3. (iii) → (d)
4. (iv) → (c)