If A and B are two sets, then `A nn (A uu B)` equals

Options

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

Explanation

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

### Step 1: Understand the Definitions
- **Union (\( A \cup B \))**: This is the set of elements that are in either set A, set B, or in both.
- **Intersection (\( A \cap (A \cup B) \))**: This is the set of elements that are common to both set A and the set \( A \cup B \).

### Step 2: Analyze the Expression
We need to find the intersection of set A with the union of sets A and B.

### Step 3: Apply the Definition of Union
The union \( A \cup B \) includes all elements from both sets A and B. Therefore, any element that is in A will also be in \( A \cup B \).

### Step 4: Find the Intersection
Now, we need to find the intersection \( A \cap (A \cup B) \). Since all elements of A are included in \( A \cup B \), the intersection will simply be all elements of A.

### Step 5: Conclusion
Thus, we conclude that:
\[ A \cap (A \cup B) = A \]

### Final Answer
The final answer is:
\[ A \cap (A \cup B) = A \]

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