How can I show that the set { } contains elements, where S is a set of n elements and P(S) is the power set of S. [SOLVED]
Last edited by posix_memalign; April 30th 2010 at 01:54 AM. Reason: Solved
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Originally Posted by posix_memalign Let S be a set of n elements and consider the power set P(S) of S. How can I show that the set { } contains elements? Here is some notation. is the number of elements is set . Thus and . For each set that are subsets of that are super-sets of i.e. Hence that is the number of wanted pairs . To count them find the sum . Do you see why? Now use the binomial expansion theorem on
Last edited by Plato; April 29th 2010 at 03:15 PM.
Originally Posted by Plato To count them find the sum . Do you see why? After you have arrived at this then it is obvious why it is but I don't see how you arrive at this statement unfortunately no.
Originally Posted by posix_memalign After you have arrived at this then it is obvious why it is but I don't see how you arrive at this statement unfortunately no. Then I must ask you if you understand that the number of subsets having as a subset is If you do then there are subsets of each ‘size’.
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