If `A=B'`, then `(AnnB)`' is ___________.

Options

A. `varphi`
B. `mu`
C. A
D. B

Answer

To solve the problem, we need to find the value of \((A \cap B)'\) given that \(A = B'\).

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given that \(A = B'\), which means that set \(A\) is the complement of set \(B\).

2. **Apply De Morgan's Law**:
According to De Morgan's Law, the complement of the intersection of two sets can be expressed as the union of their complements:
\[ (A \cap B)' = A' \cup B' \]

3. **Find \(A'\)**:
Since \(A = B'\), we need to find \(A'\):
\[ A' = (B')' = B \]
This means that the complement of \(A\) is simply \(B\).

4. **Substitute \(A'\) and \(B'\) into De Morgan's Law**:
Now we can substitute \(A'\) and \(B'\) into the equation we derived from De Morgan's Law:
\[ (A \cap B)' = A' \cup B' = B \cup B' \]

5. **Use the Identity of Sets**:
The union of a set and its complement is the universal set:
\[ B \cup B' = U \]
where \(U\) is the universal set.

6. **Conclusion**:
Therefore, we conclude that:
\[ (A \cap B)' = U \]

### Final Answer:
\((A \cap B)' = U\) (the universal set).