If X and Y are two stes than `X cap (X cap Y)` equals to

Options

A. X
B. Y
C. `phi`
D. `X cap Y`

Answer

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

### Step-by-Step Solution:

1. **Understanding the Intersection**:
- The intersection of two sets \( A \) and \( B \), denoted as \( A \cap B \), consists of all elements that are common to both sets.

2. **Applying the Intersection**:
- We first need to evaluate \( X \cap Y \). This gives us all elements that are present in both sets \( X \) and \( Y \).

3. **Finding \( X \cap (X \cap Y) \)**:
- Now, we need to find the intersection of set \( X \) with the result of \( X \cap Y \). This means we are looking for elements that are in \( X \) and also in \( (X \cap Y) \).

4. **Using the Property of Intersection**:
- By the property of intersection, we know that \( X \cap (X \cap Y) = X \cap Y \). This is because the intersection of \( X \) with any subset of \( X \) (in this case, \( X \cap Y \)) will yield that subset.

5. **Final Result**:
- Therefore, we conclude that \( X \cap (X \cap Y) = X \cap Y \).

### Conclusion:
Thus, the answer is \( X \cap Y \).