Question 1209457
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List all subsets of {A,B,C,D}
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It has one empty subset {}.


It has 4 (four) subsets consisting of one element.

These subsets are {A}, {B}, {C}, and {D}.



It has 6 (six) subsets consisting of two elements.

These subsets are {A,B}, {A,C}, {A,D}, {B,C}, {B,D}, {C,D}.



It has 4 (four) subsets consisting of three elements.

These subsets are {A,B,C}, {A,B,D}, {A,C,D}, {B,C,D}.


We obtain this list simply crossing out letter by letter from the list of 4 elements {A,B,C,D}.



Finally, the original set {A,B,C,D} has a unique subset {A,B,C,D}, which consists of 4 elements.

This subset is special: it is called "improper" subset.



        Notice that the total number of subsets is   1 + 4 + 6 + 4 + 1 = 16 = {{{2^4}}},
        including empty subset and improper subset.



It is not a random coincidence and it is not accidently.



        The general fact is that the number of all subsets of any finite set of "n" elements is   {{{2^n}}},
        including empty subset and improper subset.