## Solving Lesson 10 Page 39 Math Study Topic 10 – Kite>

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 $$C_n^0 + C_n^1 + C_n^2 + … + C_n^n = {2^n}$$