SOLUTION: A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as subsets, there are 2^n subsets of (Omega).

Question 505652: A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as subsets, there are 2^n subsets of (Omega).
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as subsets, there are 2^n subsets of (Omega).
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Consider a set with n slots for the n elements.
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There are two possibilities for each slot.
Each element of the set is either in or not in its slot.
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There are 2^n possible possible choices. So there
are 2^n different set patterns from "all elements out
of their slot" to "all elements in their slot".
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Cheers,
Stan H.
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