The power set will certainly have $2^c$ facets.This is because while generating the powet collection, we have two selections for each aspect in the original collection.Hence, $underbrace2 imes 2 imes dots 2_ extc times = 2^c$.

You are watching: If c is a set with c elements, how many elements are in the power set of c? explain your answer.


answeredApr 14, 2019goxul

One well recognize means is currently tbelow in answer. Here is one more way.

The variety of subsets with k facets in the power collection of a set via n facets is provided by the number of combinations, C(n, k), additionally called binomial coefficients.

For example, the power collection of a set via three facets, has:

C(3, 0) = 1 subset through 0 elements (the empty subset),C(3, 1) = 3 subsets through 1 facet (the singleton subsets),C(3, 2) = 3 subsets via 2 aspects (the complements of the singleton subsets),C(3, 3) = 1 subset with 3 elements (the original collection itself).

Using this partnership we have the right to compute

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making use of the formula:

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Thus, one deserve to deduce the following identity, assuming $=n$​​​​​​​

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Source:https://en.wikipedia.org/wiki/Power_set#Relation_to_binomial_theorem


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answeredDec 26, 2019smsubham
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