If n (A) =3 ,n(B)=6 and `A sube B` .Then the number of elements in `A cup B` is equal to

Options

A. 3
B. 9
C. 6
D. Non of these

Explanation

To solve the problem, we need to find the number of elements in the union of sets A and B, given that \( n(A) = 3 \), \( n(B) = 6 \), and \( A \subseteq B \).

### Step-by-step Solution:

1. **Understand the Given Information**:
- We have two sets: \( A \) and \( B \).
- The number of elements in set \( A \) is \( n(A) = 3 \).
- The number of elements in set \( B \) is \( n(B) = 6 \).
- Set \( A \) is a subset of set \( B \) (denoted as \( A \subseteq B \)).

2. **Use the Formula for Union of Two Sets**:
- The formula for the number of elements in the union of two sets is given by:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
- Here, \( n(A \cap B) \) is the number of elements in the intersection of sets \( A \) and \( B \).

3. **Determine the Intersection**:
- Since \( A \) is a subset of \( B \), all elements of \( A \) are also in \( B \). Therefore, the intersection of \( A \) and \( B \) is simply set \( A \).
- Thus, we have:
\[ n(A \cap B) = n(A) = 3 \]

4. **Substitute Values into the Formula**:
- Now, substitute the values into the union formula:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 3 + 6 - 3 \]

5. **Calculate the Result**:
- Perform the calculation:
\[ n(A \cup B) = 6 \]

6. **Final Answer**:
- The number of elements in \( A \cup B \) is \( 6 \).

### Summary:
The number of elements in \( A \cup B \) is \( 6 \).