If `A` and `B` are two sets, then `A nn (A uu B)'` is equal to - A (b) B (c) ϕ (d) A ∩ B `

Options

A. `A`
B. `B`
C. `phi`
D. `A nn B``

Explanation

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

### Step-by-Step Solution:

1. **Understand the notation**:
- \( A \cap (A \cup B)' \) means the intersection of set \( A \) with the complement of the union of sets \( A \) and \( B \).
- The complement of a set \( X \) is denoted as \( X' \) or \( X^c \) and refers to all elements not in \( X \).

2. **Find \( A \cup B \)**:
- The union \( A \cup B \) is the set of all elements that are in \( A \), in \( B \), or in both.

3. **Find \( (A \cup B)' \)**:
- The complement \( (A \cup B)' \) is the set of all elements that are not in \( A \cup B \).
- This can be expressed as \( U - (A \cup B) \), where \( U \) is the universal set containing all possible elements.

4. **Now, find \( A \cap (A \cup B)' \)**:
- We need to find the intersection of set \( A \) with the complement \( (A \cup B)' \).
- This means we are looking for elements that are in \( A \) but not in \( A \cup B \).

5. **Analyze the intersection**:
- If an element is in \( A \) and also in \( A \cup B \), it cannot be in \( (A \cup B)' \).
- Therefore, the only elements that can be in \( A \) and not in \( A \cup B \) are those that are in \( A \) but not in \( B \).

6. **Conclusion**:
- The result of \( A \cap (A \cup B)' \) is the set of elements in \( A \) that are not in \( B \), which is denoted as \( A - B \).
- However, since we are looking for the options provided, we can see that the intersection results in the empty set \( \phi \) if there are no elements in \( A \) that are not in \( B \).

### Final Answer:
The correct answer is \( \phi \) (option c).