If A and B are disjoint sets, then `A nn (A' uu B)` is equal to which one of the following?

Options

A. `phi`
B. A
C. `A uu B`
D. `A-B'`

Answer

To solve the problem, we need to find the value of \( A \cap (A' \cup B) \) given that sets \( A \) and \( B \) are disjoint.

### Step-by-step Solution:

1. **Understand the Sets**:
- \( A' \) is the complement of set \( A \), which includes all elements not in \( A \).
- Since \( A \) and \( B \) are disjoint, \( A \cap B = \emptyset \) (the intersection of \( A \) and \( B \) is the empty set).

2. **Find \( A' \cup B \)**:
- The union \( A' \cup B \) includes all elements that are either not in \( A \) or in \( B \).
- Since \( A \) and \( B \) are disjoint, \( A' \) does not include any elements from \( B \).

3. **Calculate \( A \cap (A' \cup B) \)**:
- Now, we need to find the intersection of \( A \) with \( A' \cup B \).
- The intersection \( A \cap A' \) is empty because no element can be both in \( A \) and not in \( A \).
- The intersection \( A \cap B \) is also empty because \( A \) and \( B \) are disjoint.

4. **Combine the Results**:
- Therefore, \( A \cap (A' \cup B) = (A \cap A') \cup (A \cap B) = \emptyset \cup \emptyset = \emptyset \).

5. **Conclusion**:
- Thus, \( A \cap (A' \cup B) = \emptyset \).

The answer is that \( A \cap (A' \cup B) \) is equal to the null set.

### Final Answer:
**Option A: Null Set**