Determine the Number of Subset

Try to note how to determine the following subset:

A = {1}, the number of subsets of A is 2, namely {1} and ∅.
B = {1,2}, the number of subsets of B is 4, namely {1}, {2}, {1,2}, and ∅.
C = {1,2, 3}, the number of subsets of C there are 8, namely {1}, {2}, {3}, {1,2}, {1, 3}, {2, 3}, { 1, 2, 3}, and ∅.

If you pay attention to the above, you get the following statement:

If n(A) = 1, then many sets are 2 = 2¹.
If n(B) = 2, then many of the subsets are 4 = 2²  If n(C) = 3, then many sets of parts are 8 = 2³

In this way, it can be concluded as follows:

If many members of set A are n and many subsets of A are N then N = 2ⁿ.

Thus this article. Sorry if there is a mistake.
Final words wassalamualaikum wr. wb.

Reference:

• The book Berlogika with mathematics (Umi Salamah)

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