Let A ={1,2,3,4,5,6} and B= {3,4,5,6,7,8} find `(A-B)uu(B-A)`.

Answer

To solve the problem, we need to find \( (A - B) \cup (B - A) \) where \( A = \{1, 2, 3, 4, 5, 6\} \) and \( B = \{3, 4, 5, 6, 7, 8\} \).

### Step 1: Find \( A - B \)
The operation \( A - B \) means we need to find the elements that are in set \( A \) but not in set \( B \).

- Elements in \( A \): \( 1, 2, 3, 4, 5, 6 \)
- Elements in \( B \): \( 3, 4, 5, 6, 7, 8 \)

Now, we will check each element of \( A \):
- \( 1 \) is not in \( B \) → include \( 1 \)
- \( 2 \) is not in \( B \) → include \( 2 \)
- \( 3 \) is in \( B \) → do not include
- \( 4 \) is in \( B \) → do not include
- \( 5 \) is in \( B \) → do not include
- \( 6 \) is in \( B \) → do not include

Thus, \( A - B = \{1, 2\} \).

### Step 2: Find \( B - A \)
The operation \( B - A \) means we need to find the elements that are in set \( B \) but not in set \( A \).

- Elements in \( B \): \( 3, 4, 5, 6, 7, 8 \)
- Elements in \( A \): \( 1, 2, 3, 4, 5, 6 \)

Now, we will check each element of \( B \):
- \( 3 \) is in \( A \) → do not include
- \( 4 \) is in \( A \) → do not include
- \( 5 \) is in \( A \) → do not include
- \( 6 \) is in \( A \) → do not include
- \( 7 \) is not in \( A \) → include \( 7 \)
- \( 8 \) is not in \( A \) → include \( 8 \)

Thus, \( B - A = \{7, 8\} \).

### Step 3: Find \( (A - B) \cup (B - A) \)
Now we need to find the union of the two sets we found:

- \( A - B = \{1, 2\} \)
- \( B - A = \{7, 8\} \)

The union \( (A - B) \cup (B - A) \) combines all unique elements from both sets:

\[ (A - B) \cup (B - A) = \{1, 2\} \cup \{7, 8\} = \{1, 2, 7, 8\} \]

### Final Answer
Thus, the final result is:

\[ (A - B) \cup (B - A) = \{1, 2, 7, 8\} \]

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