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 "If A and B are two sets, then A ∩ (A ∪ B) equals", we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Sets**:
- Let A and B be two sets.
- A ∪ B (A union B) represents all elements that are in A, in B, or in both.
- A ∩ (A ∪ B) (A intersection (A union B)) represents all elements that are in both A and (A union B).

2. **Visualize with a Venn Diagram**:
- Draw a Venn diagram with two overlapping circles, one for set A and one for set B.
- The area covered by both circles represents A ∪ B.

3. **Identify A ∪ B**:
- The union A ∪ B includes all elements from both sets A and B. This means every element that is in A is also included in A ∪ B.

4. **Find the Intersection**:
- Now, we need to find A ∩ (A ∪ B). This means we are looking for elements that are in set A and also in the union of A and B.
- Since every element of A is already included in A ∪ B, the intersection will simply be all elements of A.

5. **Conclusion**:
- Therefore, A ∩ (A ∪ B) = A.

### Final Answer:
A ∩ (A ∪ B) = A

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