https://file.aiquickdraw.com/mathbot/file/17270133630012n0susax.jpg

Here is the Venn diagram illustrating the equation:

\[
A \cap (B \oplus C) = (A \cap B) \oplus (A \cap C)
\]

- The diagram shows the regions for sets \(A\), \(B\), and \(C\).
- The symmetric difference \(\oplus\) represents the regions that belong to one set but not both.
- The left-hand side (LHS) represents the intersection of \(A\) with the symmetric difference \(B \oplus C\).
- The right-hand side (RHS) shows the symmetric difference between \(A \cap B\) and \(A \cap C\), which equals the LHS, visually confirming the equation.

Do you have any further questions or would you like more details?

Here are five follow-up questions:
1. How does the symmetric difference \(B \oplus C\) differ from a simple union?
2. Can you apply this identity to specific sets, like using numerical values?
3. How does the Venn diagram change if \(B\) and \(C\) are disjoint?
4. What is the geometric interpretation of symmetric difference in higher dimensions?
5. How would the Venn diagram change if \(A\) were a subset of \(B\)?

**Tip:** Symmetric difference is useful in logic and set theory because it simplifies statements involving exclusive conditions.

Make a Venn diagram for the equation A ∩ (B ⊕ C) = (A ∩ B) ⊕ (A ∩ C).

Explore how to create a Venn diagram for the equation A ∩ (B ⊕ C) = (A ∩ B) ⊕ (A ∩ C). Learn the key concepts of symmetric difference, intersection, and their relationships in set theory. Suitable for students in Grades 9-12.

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