The symmetric difference of sets A and B is equal to
(i) `(A-B)uu(B-A)`
(ii) `(B-A)uuB`
(iii) `(AuuB)-(AnnB)`
(iv) `(AuuB)nn(AnnB)`

Options

A. `(A-B)uu(B-A)`
B. `(B-A)uuB`
C. `(AuuB)-(AnnB)`
D. `(AuuB)nn(AnnB)`

Answer

To solve the question regarding the symmetric difference of sets A and B, we will follow these steps:

### Step 1: Understand the concept of symmetric difference
The symmetric difference of two sets A and B, denoted as \( A \Delta B \), is defined as the set of elements that are in either of the sets but not in their intersection. In simpler terms, it includes elements that are in A or in B but not in both.

### Step 2: Write the formula for symmetric difference
The formula for the symmetric difference can be expressed as:
\[ A \Delta B = (A - B) \cup (B - A) \]
This means we take elements that are in A but not in B and combine them with elements that are in B but not in A.

### Step 3: Analyze the given options
Now, we will analyze each option provided in the question to see which one matches our derived formula.

1. **Option (i)**: \( (A - B) \cup (B - A) \)
This matches our derived formula for symmetric difference.

2. **Option (ii)**: \( (B - A) \cup B \)
This does not represent the symmetric difference, as it includes all elements of B.

3. **Option (iii)**: \( (A \cup B) - (A \cap B) \)
This is another valid expression for the symmetric difference, as it represents all elements in A or B minus those that are in both.

4. **Option (iv)**: \( (A \cup B) \cap (A \cap B) \)
This represents the intersection of A and B, which is not the symmetric difference.

### Step 4: Identify the correct options
From our analysis:
- Option (i) \( (A - B) \cup (B - A) \) is correct.
- Option (iii) \( (A \cup B) - (A \cap B) \) is also correct.

### Conclusion
The symmetric difference of sets A and B is equal to:
- **Option (i)**: \( (A - B) \cup (B - A) \)
- **Option (iii)**: \( (A \cup B) - (A \cap B) \)