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For a set with n items, the number of elements in its power set is the total number of possible subsets of that set. So how many subsets are there?
Consider this. The A= {x1,x2,..xn} be your set of n elenents. While constructing a subset S, for each element we are faced with a choice: do we include it or not. Since there are n elenents, we get n choices each with 2 possible outcomes. Thus the total number of ways to do it will be 2n .
Thus for 4 elements the number of subsets are 2⁴=16.
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