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Math Help - Crossing power sets

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    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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