If `f:A rarrB` is bijective function such that `n(A)=10,` then `n(B)=?`

Answer

To solve the problem, we need to understand the properties of a bijective function. A function \( f: A \rightarrow B \) is called bijective if it is both one-to-one (injective) and onto (surjective). This means that every element in set \( A \) maps to a unique element in set \( B \), and every element in set \( B \) is mapped by some element in set \( A \).

Given that \( n(A) = 10 \), where \( n(A) \) represents the number of elements in set \( A \), we need to find \( n(B) \), the number of elements in set \( B \).

### Step-by-Step Solution:

1. **Understand the Definition of Bijective Functions**:
A bijective function means that there is a perfect pairing between the elements of set \( A \) and set \( B \). Each element in \( A \) corresponds to exactly one element in \( B \) and vice versa.

2. **Use the Property of Bijective Functions**:
For a bijective function \( f: A \rightarrow B \), the number of elements in \( A \) is equal to the number of elements in \( B \). This can be expressed mathematically as:
\[ n(A) = n(B) \]

3. **Substitute the Known Value**:
We know from the problem statement that \( n(A) = 10 \). Therefore, substituting this value into the equation gives:
\[ n(B) = n(A) = 10 \]

4. **Conclusion**:
Thus, the number of elements in set \( B \) is also 10. Therefore, we conclude:
\[ n(B) = 10 \]

### Final Answer:
The number of elements in set \( B \) is \( n(B) = 10 \).

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