If A is a finite set with m elements then prove that the number of subsets is`2^m`

Explanation

Let `A` contains `1` element such that `A = {1}`.

Then, subsets of `A = {},{1} `.

`:.` Number of subsets of `A = 2 =2^1.`

Let `A` contains `2` elements such that `A = {1,2}`.

Then, subsets of `A = {},{1},{2},{1,2}. `

`:.` Number of subsets of `A = 4 =2^2.`

Let `A` contains `3` elements such that `A = {1,2,3}`.

Then, subsets of `A = {},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}. `

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