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 result of the expression \( A \cap (A \cup B) \).

### Step-by-Step Solution:

1. **Understand the Symbols**:
- \( A \cap B \) denotes the intersection of sets A and B, which includes all elements that are in both A and B.
- \( A \cup B \) denotes the union of sets A and B, which includes all elements that are in either A, B, or both.

2. **Identify the Expression**:
- We need to evaluate \( A \cap (A \cup B) \).

3. **Apply the Definition of Union**:
- The union \( A \cup B \) contains all elements that are in A, all elements that are in B, and any elements that are in both.

4. **Evaluate the Intersection**:
- Now, we need to find the intersection of A with the union \( A \cup B \).
- The intersection \( A \cap (A \cup B) \) will include all elements that are in A and also in the set \( A \cup B \).

5. **Simplify the Expression**:
- Since all elements of A are included in \( A \cup B \), the intersection \( A \cap (A \cup B) \) will simply be all elements of A.
- Therefore, \( A \cap (A \cup B) = A \).

### Final Result:
The result of \( A \cap (A \cup B) \) is \( A \).