If `A={1,2,3,4,5,6}` and `B={2,4,5,6,8,9,10}`, then `A DeltaB` is equal to

Options

A. {1,3}
B. {8,9,10}
C. {2,4,5,6}
D. {1,3,8,9,10}

Answer

To solve the problem of finding \( A \Delta B \) (the symmetric difference of sets A and B), we will follow these steps:

### Step 1: Define the sets
Given:
- \( A = \{1, 2, 3, 4, 5, 6\} \)
- \( B = \{2, 4, 5, 6, 8, 9, 10\} \)

### Step 2: Understand the symmetric difference
The symmetric difference \( A \Delta B \) is defined as:
\[ A \Delta B = (A - B) \cup (B - A) \]
Where:
- \( A - B \) is the set of elements in A that are not in B.
- \( B - A \) is the set of elements in B that are not in A.

### Step 3: Calculate \( A - B \)
To find \( A - B \):
- We look for elements in A that are not in B.
- From set A:
- 1 is not in B
- 2 is in B
- 3 is not in B
- 4 is in B
- 5 is in B
- 6 is in B

Thus, \( A - B = \{1, 3\} \).

### Step 4: Calculate \( B - A \)
To find \( B - A \):
- We look for elements in B that are not in A.
- From set B:
- 2 is in A
- 4 is in A
- 5 is in A
- 6 is in A
- 8 is not in A
- 9 is not in A
- 10 is not in A

Thus, \( B - A = \{8, 9, 10\} \).

### Step 5: Combine the results
Now we combine the results of \( A - B \) and \( B - A \):
\[ A \Delta B = (A - B) \cup (B - A) = \{1, 3\} \cup \{8, 9, 10\} \]

### Step 6: Write the final result
The final result is:
\[ A \Delta B = \{1, 3, 8, 9, 10\} \]

### Conclusion
Thus, the answer is option D: \( \{1, 3, 8, 9, 10\} \).

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