# Crossing power sets

• January 29th 2009, 01:19 PM
nikie1o2
Crossing power sets
Ok so I have the problem:

let A and B be finite sets with lAl=m and lBl=n.
Express lP(A) X P(B)l and lP(A X B)l in terms of m and n
• January 29th 2009, 01:30 PM
Plato
Quote:

Originally Posted by nikie1o2
let A and B be finite sets with lAl=m and lBl=n.
Express lP(A) X P(B)l and lP(A X B)l in terms of m and n

$\begin{gathered}
\left| K \right| = n\;\& \;\left| J \right| = m\; \Rightarrow \;\left| {K \times J} \right| = (n)(m) \hfill \\
\left| {\mathbb{P}(K)} \right| = 2^n \;\& \;\left| {\mathbb{P}(J)} \right| = 2^m \; \Rightarrow \;\left| {\mathbb{P}(K) \times \mathbb{P}(J)} \right| = \left( {2^n } \right)\left( {2^m } \right) = 2^{n + m} \hfill \\
\end{gathered}$

And also $\left| {\mathbb{P}(K \times J)} \right| = 2^{nm}$