Prove-that-for-any-set-A-containing-n-elements-P-A-2-n-

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

Prove that for any set A containing n

elements, ∣ P (A) ∣= 2^{n} .

Answered by AST last updated on 16/Nov/23

C_{0}^{n} +^{n} C_{1} +^{n} C_{2} + \dots +^{n} C_{n} = {(1 + 1)}^{n} = 2^{n} =∣ P (A) ∣

s i n c e ∣ P (A) ∣= T o t a l n u m b e r o f s u b s e t s w i t h

c a r d i n a l i t y o f 0 t o n .

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