If `A` and `B` are disjoint sets, then `n(A cap B) = ?`

Options

A. `phi`
B. `n (A) +n(B)`
C. `n(A)`
D. `n(B)`

Answer

To solve the problem, we need to understand the concept of disjoint sets and the notation used in set theory.

### Step-by-Step Solution:

1. **Understanding Disjoint Sets**:
- Two sets are said to be disjoint if they have no elements in common. This means that the intersection of the two sets is empty.

2. **Notation**:
- The intersection of sets A and B is denoted by \( A \cap B \).
- The number of elements in the intersection of sets A and B is denoted by \( n(A \cap B) \).

3. **Applying the Definition**:
- Since A and B are disjoint, by definition, there are no elements that belong to both sets. Therefore, the intersection \( A \cap B \) is an empty set.

4. **Finding the Number of Elements**:
- The number of elements in an empty set is 0. Thus, we can conclude that:
\[ n(A \cap B) = 0 \]

### Final Answer:
\[ n(A \cap B) = 0 \]