Prove, by Induction, that the number of all the subsets of a set containing n distinct elements, is `2^n`.

What is the total number of proper subsets of a set containing n elements ?

The number of elements of the power set of a set containing n elements is

Prove by Induction, that 2^n ltn ! for all nge4 .

Prove that the number of all subsets of a finite set of n element is 2^(n) .

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements :

Fill in the blank: The total number of injective functions that can be defined form a set A contaiing n distinct elements onto itself is _______.

Prove by Induction, for all n in N : 2^n >n .

Prove by Induction, for all n in N : 2^n < 3^n .