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The image shows a mathematical problem about the **symmetric difference** of two sets, followed by a specific problem for two given sets \( A \) and \( B \).

1. **Definition of Symmetric Difference**: The symmetric difference of two sets \( A \) and \( B \), denoted \( A \Delta B \), is the set of elements that are in either \( A \) or \( B \), but not in both. Mathematically, it is expressed as:
   \[
   A \Delta B = (A - B) \cup (B - A)
   \]
   Here, \( A - B \) represents the set of elements in \( A \) but not in \( B \), and similarly \( B - A \) represents the set of elements in \( B \) but not in \( A \).

2. **Given Sets**:
   \[
   A = \{1, 2, 3, 4, 5, 6\}, \quad B = \{2, 4, 6, 8\}
   \]
   
   The problem asks you to **show that \( A - B \neq B - A \)**.

### Solution Steps:
1. **Find \( A - B \)**:
   \[
   A - B = \{1, 2, 3, 4, 5, 6\} - \{2, 4, 6, 8\} = \{1, 3, 5\}
   \]
   This represents the elements in \( A \) that are not in \( B \).

2. **Find \( B - A \)**:
   \[
   B - A = \{2, 4, 6, 8\} - \{1, 2, 3, 4, 5, 6\} = \{8\}
   \]
   This represents the elements in \( B \) that are not in \( A \).

3. **Conclusion**:
   Clearly, \( A - B = \{1, 3, 5\} \) and \( B - A = \{8\} \), which are not equal. Hence, \( A - B \neq B - A \).

Would you like more details or have any questions?

### Related Questions:
1. What is the difference between symmetric difference and union of sets?
2. Can the symmetric difference of two sets ever be empty? If so, when?
3. How does symmetric difference differ from intersection of sets?
4. How do you prove \( A \Delta B = (A \cup B) - (A \cap B) \)?
5. How does the operation of symmetric difference behave with more than two sets?

### Tip:
Remember that symmetric difference is **commutative**, meaning \( A \Delta B = B \Delta A \), even though individual set differences like \( A - B \) and \( B - A \) may not be equal.

Define Symmetric Difference of two sets. Let A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}, then show that A - B ≠ B - A.

Learn about the symmetric difference of two sets A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}, and how to show that A - B ≠ B - A. Understand key set theory concepts, including symmetric difference and set difference, with detailed explanations.

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