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

Answer

To solve the problem, we need to find the value of \( A \cap (A \cup B) \), where \( A \) and \( B \) are two sets.

### Step-by-Step Solution:

1. **Understanding the Union of Sets**:
- The union of two sets \( A \) and \( B \), denoted as \( A \cup B \), is the set of all elements that are in \( A \), in \( B \), or in both.

2. **Understanding the Intersection of Sets**:
- The intersection of two sets \( A \) and \( C \), denoted as \( A \cap C \), is the set of all elements that are common to both sets \( A \) and \( C \).

3. **Applying the Definitions**:
- We need to find \( A \cap (A \cup B) \).
- Since \( A \cup B \) includes all elements of \( A \) and all elements of \( B \), the intersection \( A \cap (A \cup B) \) will include all elements that are in \( A \) because all elements of \( A \) are also in \( A \cup B \).

4. **Conclusion**:
- Therefore, \( A \cap (A \cup B) = A \).

### Final Answer:
\[ A \cap (A \cup B) = A \]