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The problem is asking to evaluate the expression \( X \cup (X \cap Y) \) where \( X \) and \( Y \) are two sets.

### Explanation:
- \( X \cap Y \) represents the intersection of sets \( X \) and \( Y \), i.e., the set of elements that are in both \( X \) and \( Y \).
- \( X \cup (X \cap Y) \) represents the union of \( X \) with the intersection of \( X \) and \( Y \).

Now, consider the following logic:
- Every element of \( X \cap Y \) is already in \( X \), since the intersection is a subset of \( X \).
- Therefore, the union of \( X \) with \( X \cap Y \) will simply give back the set \( X \) because all elements of \( X \cap Y \) are already included in \( X \).

Thus, we conclude:
\[ X \cup (X \cap Y) = X \]

### The correct answer is \( \boxed{A} \).

Would you like more details on set operations or related concepts?

Here are 5 follow-up questions:
1. What is the difference between the union and intersection of two sets?
2. Can you give an example where \( X \cup (X \cap Y) \neq X \cup Y \)?
3. How would you prove that \( X \cup (X \cap Y) = X \) using set properties?
4. What happens to the union and intersection if \( X \) and \( Y \) are disjoint sets?
5. Can the union of two sets ever result in a set smaller than the individual sets?

**Tip:** Remember that the union of two sets \( A \cup B \) includes all elements from both \( A \) and \( B \), while the intersection \( A \cap B \) includes only the common elements.

Let X, Y be two sets. Then X ∪ (X ∩ Y) is?

Explore how to solve the set operation X ∪ (X ∩ Y) and understand the union and intersection of sets with a detailed step-by-step explanation. This problem focuses on set theory concepts like subset theorem and distributive law. Suitable for students in Grades 9-12.

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