Topic
Given the set \(A = \left\{ {{x_1};{x_2};{x_3};…;{x_n}} \right\}\) has n elements. Calculate the number of subsets of A
Solution method – See details
The number of subsets of a set of n elements is \({2^n}\)
Detailed explanation
The number of subsets of a set of n elements is \({2^n}\)
Indeed,
+ The number of subsets with 0 elements of set A is: \(C_n^0\)
+ The number of subsets with 1 element of set A is: \(C_n^1\)
+ The number of subsets with 2 elements of set A is: \(C_n^2\)
…
+ The number of subsets with n elements of set A is: \(C_n^n\)
=> The number of subsets of the set of n elements is \(C_n^0 + C_n^1 + C_n^2 + … + C_n^n = {2^n}\)
