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I am supposed to show that the number of proper subsets of S = {a1, a2, ... an} is 2^n - 1.

I know that the number of subsets of S is 2^n. And I know also know that the number of proper subsets of S is 2^n - 1 since S is not a proper subset of itself.

But how do I show that? I could show this by brute force. But I can't seem to think of a way to show it in a more efficient way.

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# The Number Of Proper Subsets is 2^n - 1

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