Question

If a set A and n elements then find the number of elements in its power set P(A).

Answer 1

The power set of set A is a collection of all subsets of A. 

For example: if the set A is {1, 2} then all possible subsets of A would be {} (empty set), {1}, {2}, {1, 2} 

Hence power set of A that is P(A) will be {ϕ, {1}, {2}, {1,2}} 

Now if the number of elements in set A is n then the number of elements in power set of A P(A) is 2ⁿ