If `A={1,2,3,4,5,6,7,8}` and `B={1,3,4,6,7,8,9}` then

Options

A. (a) `A-B=B-A`
B. (b) `A-B ne B-A`
C. (c) `(A-B) uu (B-A)=B`
D. (d) none of these

Answer

To solve the problem, we need to find the differences between the two sets \( A \) and \( B \), and then evaluate the options provided.

Given:
- \( A = \{1, 2, 3, 4, 5, 6, 7, 8\} \)
- \( B = \{1, 3, 4, 6, 7, 8, 9\} \)

### Step 1: Find \( A - B \)

The set difference \( A - B \) consists of elements that are in \( A \) but not in \( B \).

- Elements in \( A \): \( 1, 2, 3, 4, 5, 6, 7, 8 \)
- Elements in \( B \): \( 1, 3, 4, 6, 7, 8, 9 \)

Now, we will check each element of \( A \):
- \( 1 \) is in \( B \) (not included)
- \( 2 \) is not in \( B \) (included)
- \( 3 \) is in \( B \) (not included)
- \( 4 \) is in \( B \) (not included)
- \( 5 \) is not in \( B \) (included)
- \( 6 \) is in \( B \) (not included)
- \( 7 \) is in \( B \) (not included)
- \( 8 \) is in \( B \) (not included)

Thus, \( A - B = \{2, 5\} \).

### Step 2: Find \( B - A \)

The set difference \( B - A \) consists of elements that are in \( B \) but not in \( A \).

Now, we will check each element of \( B \):
- \( 1 \) is in \( A \) (not included)
- \( 3 \) is in \( A \) (not included)
- \( 4 \) is in \( A \) (not included)
- \( 6 \) is in \( A \) (not included)
- \( 7 \) is in \( A \) (not included)
- \( 8 \) is in \( A \) (not included)
- \( 9 \) is not in \( A \) (included)

Thus, \( B - A = \{9\} \).

### Step 3: Compare \( A - B \) and \( B - A \)

Now we compare the two results:
- \( A - B = \{2, 5\} \)
- \( B - A = \{9\} \)

Clearly, \( A - B \) is not equal to \( B - A \).

### Step 4: Evaluate the Options

1. **Option A**: \( A - B = B - A \) → False
2. **Option B**: \( A - B \neq B - A \) → True
3. **Option C**: \( A - B \cup B - A = B \) → False
4. **Option D**: None of these → False

### Conclusion

The correct answer is **Option B**: \( A - B \) is not equal to \( B - A \).