If n(A × B)=200 and n(A)=50, Find the Number of Elements in P(B)
Question
If
\[ n(A\times B)=200 \]
and
\[ n(A)=50, \]
then the number of elements in \( P(B) \) is ……………………….
Solution
We know that:
\[ n(A\times B)=n(A)\times n(B) \]
Substituting the given values:
\[ 200=50\times n(B) \]
\[ n(B)=\frac{200}{50}=4 \]
The number of elements in the power set of a set having \( n \) elements is:
\[ 2^n \]
Therefore,
\[ n(P(B))=2^{4}=16 \]
Hence, the required answer is:
\[ \boxed{16} \]