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.