The set `AcapA` is :

Options

A. `phi`
B. U
C. A
D. A'

Answer

To solve the question regarding the intersection of the set A with itself (denoted as \( A \cap A \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Intersection**: The intersection of two sets, denoted as \( A \cap B \), consists of all the elements that are common to both sets A and B.

**Hint**: Remember that the intersection only includes elements that appear in both sets.

2. **Identifying Set A**: Let’s assume set A contains certain elements. For example, let’s say \( A = \{1, 2, 3\} \).

**Hint**: You can choose any elements for set A, but for simplicity, we will use this example.

3. **Finding \( A \cap A \)**: Now, we need to find the intersection of set A with itself, which is \( A \cap A \). Since both sets are exactly the same, all elements in A will be common.

**Hint**: When you intersect a set with itself, all elements will be present in the intersection.

4. **Conclusion**: Therefore, \( A \cap A = A \). In our example, \( A \cap A = \{1, 2, 3\} \).

**Hint**: The result of the intersection of a set with itself is always the set itself.

5. **Evaluating Options**: If we have options provided (as mentioned in the video), we can conclude that the correct answer is the set A itself.

**Hint**: Look for the option that states the intersection is equal to A.

### Final Answer:
The set \( A \cap A \) is equal to \( A \).