If `A = {1,2,3} and B={2,3,4}`, then the symmetric difference of A and B is :

Options

A. `{1,4}`
B. `{2,3}`
C. `{4}`
D. `{1}`

Answer

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

### Step 1: Identify the sets
We have:
- Set A = {1, 2, 3}
- Set B = {2, 3, 4}

### Step 2: Calculate A - B
The operation A - B means we need to remove the elements of B from A.
- Elements of A: {1, 2, 3}
- Elements of B: {2, 3}

Removing 2 and 3 from A leaves us with:
- A - B = {1}

### Step 3: Calculate B - A
The operation B - A means we need to remove the elements of A from B.
- Elements of B: {2, 3, 4}
- Elements of A: {1, 2, 3}

Removing 2 and 3 from B leaves us with:
- B - A = {4}

### Step 4: Calculate the union of (A - B) and (B - A)
Now, we take the union of the results from Step 2 and Step 3:
- A - B = {1}
- B - A = {4}

The union of {1} and {4} is:
- A Δ B = {1, 4}

### Final Result
The symmetric difference of sets A and B is:
- A Δ B = {1, 4}

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