The symmetric difference of sets A and B is equal to

Options

A. a. `(A-B)nn(B-A)`
B. b. `(A-B)uu(B-A)`
C. c. `(AuuB)-(AnnB)`
D. d. `((AuuB)-B)uu((AuuB)-A)`

Answer

To find the symmetric difference of sets A and B, we can follow these steps:

### Step 1: Understand the Definition of Symmetric Difference
The symmetric difference of two sets A and B, denoted as A Δ B, is defined as the set of elements that are in either of the sets A or B but not in their intersection.

### Step 2: Calculate A - B
First, we need to find the elements that are in set A but not in set B. This is represented as:
\[ A - B = \{ x \in A \mid x \notin B \} \]

### Step 3: Calculate B - A
Next, we find the elements that are in set B but not in set A. This is represented as:
\[ B - A = \{ x \in B \mid x \notin A \} \]

### Step 4: Take the Union of the Results
Now, we take the union of the two results from Step 2 and Step 3. The union of two sets combines all unique elements from both sets. Thus, we have:
\[ A Δ B = (A - B) \cup (B - A) \]

### Conclusion
Therefore, the symmetric difference of sets A and B is given by:
\[ A Δ B = (A - B) \cup (B - A) \]

### Final Answer
The correct option is **B: A - B union B - A**.

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