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#1

$Old$ October 31st, 2009, 04:14 PM

kashifzaidi $kashifzaidi is offline$

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$Default$ Cardinality

Show that if sets A and B have the same cardinality,
then P(A) and P(B) have the same cardinality.

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$Old$ October 31st, 2009, 04:56 PM

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Originally Posted by kashifzaidi $View Post$

Show that if sets A and B have the same cardinality,
then P(A) and P(B) have the same cardinality.

$\exists\,\;bijection\,\;f:A\rightarrow B\Longrightarrow$ $F:P(A)\rightarrow P(B)\,,\;\;F(X):=\{f(x)\,;\;x\in X\subset A\}\subset B$ $\,\,is\,\,a\,\,bijection$

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cardinality, discrete math

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