If X and Y are two sets, then `Xnn(XuuY)` equals

Options

A. X
B. Y
C. `phi`
D. None of these

Answer

To solve the problem of finding \( X \cap (X \cup Y) \), we can follow these steps:

### Step 1: Understand the Sets
We have two sets, \( X \) and \( Y \). We need to find the intersection of set \( X \) with the union of sets \( X \) and \( Y \).

### Step 2: Define the Union
The union of two sets \( X \) and \( Y \), denoted as \( X \cup Y \), includes all elements that are in \( X \), in \( Y \), or in both.

### Step 3: Define the Intersection
The intersection of two sets \( A \) and \( B \), denoted as \( A \cap B \), includes all elements that are common to both sets.

### Step 4: Apply the Definitions
Now, we need to find \( X \cap (X \cup Y) \). This means we are looking for all elements that are in both \( X \) and \( (X \cup Y) \).

### Step 5: Analyze the Intersection
Since \( (X \cup Y) \) contains all elements of \( X \) (as well as any elements from \( Y \)), the intersection \( X \cap (X \cup Y) \) will simply be all elements of \( X \).

### Step 6: Conclusion
Thus, we conclude that:
\[ X \cap (X \cup Y) = X \]

### Final Answer
The answer is \( X \).

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