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Question Number 200284 by depressiveshrek last updated on 16/Nov/23

$$\mathrm{Prove}\mathrm{that}\mathrm{for}\mathrm{any}\mathrm{set}A\mathrm{containing}n$$$$\mathrm{elements},\mid \mathcal{P}\left(A\right)\mid =2^n.$$

Answered by deleteduser1 last updated on 16/Nov/23

$$C_0^n{+}^n{C}_1{+}^n{C}_2+...{+}^n{C}_n={(1+1)}^n=2^n=\mid \mathcal{P}\left(A\right)\mid$$$$since\mid \mathcal{P}\left(A\right)\mid =Totalnumberofsubsetswith$$$$cardinalityof0ton.$$

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