If `n(A) = 10,n(B) = 6 and n( C ) =5 ` for three disjoint sets `A,B,C` then `n (A cup B cup C)` equals

Options

A. 21
B. 11
C. 1
D. 9

Explanation

To solve the problem, we need to find the number of elements in the union of three disjoint sets A, B, and C. Given the values:

- \( n(A) = 10 \)
- \( n(B) = 6 \)
- \( n(C) = 5 \)

Since the sets A, B, and C are disjoint, it means they have no elements in common. Therefore, the formula for the number of elements in the union of disjoint sets simplifies to the sum of the number of elements in each set.

### Step-by-Step Solution:

1. **Identify the number of elements in each set**:
- \( n(A) = 10 \)
- \( n(B) = 6 \)
- \( n(C) = 5 \)

2. **Apply the formula for the union of disjoint sets**:
Since A, B, and C are disjoint, we can use the formula:
\[ n(A \cup B \cup C) = n(A) + n(B) + n(C) \]

3. **Substitute the values into the formula**:
\[ n(A \cup B \cup C) = 10 + 6 + 5 \]

4. **Calculate the sum**:
\[ n(A \cup B \cup C) = 21 \]

Thus, the number of elements in the union of sets A, B, and C is **21**.

### Final Answer:
\[ n(A \cup B \cup C) = 21 \]