The symmetric difference of `A={0,1,2}` and `B={2,3,4}` is

Options

A. `{0,1}`
B. `{3,4}`
C. `{0,1,3,4}`
D. `{0,1,2,3,4}`

Answer

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

### Step 1: Define the Sets
We have:
- Set \( A = \{0, 1, 2\} \)
- Set \( B = \{2, 3, 4\} \)

### Step 2: Identify the Elements in Each Set
List the elements in both sets:
- Elements in \( A \): 0, 1, 2
- Elements in \( B \): 2, 3, 4

### Step 3: Find the Intersection of Sets \( A \) and \( B \)
The intersection of \( A \) and \( B \) is the set of elements that are common to both sets:
- \( A \cap B = \{2\} \)

### Step 4: Find the Difference \( A - B \) and \( B - A \)
Now, we will find the elements that are in \( A \) but not in \( B \) and vice versa:
- \( A - B = \{0, 1\} \) (elements in \( A \) that are not in \( B \))
- \( B - A = \{3, 4\} \) (elements in \( B \) that are not in \( A \))

### Step 5: Combine the Differences
The symmetric difference \( A \Delta B \) is defined as:
\[ A \Delta B = (A - B) \cup (B - A) \]
So we combine the results from the previous step:
\[ A \Delta B = \{0, 1\} \cup \{3, 4\} = \{0, 1, 3, 4\} \]

### Step 6: Final Answer
Thus, the symmetric difference of sets \( A \) and \( B \) is:
\[ A \Delta B = \{0, 1, 3, 4\} \]