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## Homework Statement

Prove that if a set a contains n elements, then the number of different subsets of A is equal to 2

^{n}.

## The Attempt at a Solution

I know how to prove with just combinatorics, where to construct a subset, each element is either in the set or not, leading to 2

^{n}subsets. I want to know how to prove it with mathematical induction though. How would I start?

I figured this using summation notation:

[itex]\sum^{k=0}_{n}[/itex] (n k)=2

^{n}