`A-(A-B)'=`

Answer

To solve the expression \( A - (A - B)' \), we will follow a systematic approach using set theory concepts.

### Step-by-Step Solution:

1. **Understand the Expression**:
We need to evaluate \( A - (A - B)' \). Here, \( (A - B)' \) denotes the complement of the set \( A - B \).

2. **Find \( A - B \)**:
The set \( A - B \) consists of all elements that are in set \( A \) but not in set \( B \).

3. **Determine \( (A - B)' \)**:
The complement \( (A - B)' \) includes all elements that are not in \( A - B \). This means it includes:
- All elements in set \( B \)
- All elements not in set \( A \)

In terms of a universal set \( U \), we can express it as:
\[ (A - B)' = U - (A - B) \]

4. **Substitute into the Original Expression**:
Now we substitute \( (A - B)' \) back into the original expression:
\[ A - (A - B)' = A - (U - (A - B)) \]

5. **Simplify the Expression**:
This can be further simplified:
\[ A - (U - (A - B)) = A \cap (A - B) \]
This means we are taking the intersection of set \( A \) with the elements that are not in \( A - B \).

6. **Final Result**:
The result \( A \cap (A - B) \) simplifies to:
\[ A \cap B \]
Thus, the final answer is:
\[ A - (A - B)' = A \cap B \]