September 4th, 2008, 10:28 AM  #1 
Newbie Joined: Sep 2008 Posts: 3 Thanks: 0  abstract alg
Please help me figure out how to get started with this problem.. For every positive integer n, prove that a set with exactly n elements has exactly 2^n subsets (counting the empty set and entire set). 
September 4th, 2008, 11:24 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: abstract alg
Try induction. The case for n=1 is simple; for n>1, let the set S have n elements and subsets, and let then for each subset both and are subsets of the set which contains n+1 elements. Moreover, these subsets are all the possible subsets of (you will need to show this); since there are two for each , and there are possible subsets , there must be possible subsets of the set 

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