If X and Y are two sets and X' denotes the complement of X then `Xcap(XuuY)` is equal to :

Options

A. X
B. y
C. `phi`
D. `XcapY`.

Answer

To solve the problem, we need to find the value of \( X \cap (X \cup Y) \).

### Step-by-Step Solution:

1. **Understanding the Sets**:
- Let \( X \) and \( Y \) be two sets.
- The notation \( X' \) represents the complement of set \( X \), but we will not need it for this specific problem.

2. **Finding \( X \cup Y \)**:
- The union of sets \( X \) and \( Y \), denoted as \( X \cup Y \), includes all elements that are in \( X \), in \( Y \), or in both.
- Therefore, \( X \cup Y = \{ x \in X \} \cup \{ y \in Y \} \).

3. **Finding \( X \cap (X \cup Y) \)**:
- The intersection of set \( X \) with the union \( (X \cup Y) \) includes all elements that are in both \( X \) and \( (X \cup Y) \).
- Since all elements of \( X \) are also included in \( (X \cup Y) \), we have:
\[ X \cap (X \cup Y) = X \]

4. **Conclusion**:
- The final result is that \( X \cap (X \cup Y) = X \).

### Final Answer:
\[ X \cap (X \cup Y) = X \]