Crossing power sets

**nikie1o2** · January 29th 2009, 01:19 PM

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

**Plato** · January 29th 2009, 01:30 PM

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

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

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

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