Explain proof for the total number of all subsets of containing n elements is 2n.

To explain this theorem

Let us consider a set  A consisting of 5 elements.

n(A)=5.

 No. Of Subsets containing no element=⁵C₀

 No. Of Subsets  containing  1 elements=⁵C₁

No of subsets containing 2 elements=⁵C₂

No of subsets containing 3 elements=5C₃

No of subsets containing 4 elements=⁵C₄

No of subsets containing 5 elements=⁵C₅

 

⁵C₀+⁵C₁+⁵C₂+⁵C₃+⁵C₄₊⁵C₅= 32   = 2⁵

^{Hence proved.....}