The total number of subsets of a Finite Set containing n elements is 2ⁿ
Theorem 3
The total number of subsets of a finite set containing n elements is 2ⁿ.
Proof
Let A be a finite set containing n elements.Let 0 ≤ r ≤ n. Consider those subset,of A that have r elements each.We know that the number of ways in which r elements can be chosen out of n elements is nCr . Therefore, the number of subsets of A having r elements each is nCr . Hence, the total number of subsets of A is nC0 + nC1 +nC2 +… +nCn = (1 + 1)ⁿ = 2ⁿ [By binomial theorem ]
We will discuss later in permutation and combination chapter in brief.
We will discuss later in permutation and combination chapter in brief.