The number of all possible subsets of a set containing n elements ?

Explanation

Let given set be `A={a_(1),a_(2),..,a_(n)}`
This set has n elements .
Now subsets can be formed using none, one , two or all elements of the set.
That means for subset zero, one or more elements may be selected.
So, for any element there are two possibilities either it will be selected or not selected.
Therefore, total number of subsets
=number of possibilities of all elements
`=2xx2xx2xx`..n times
`=2^(n)`