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.

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 making use of the formula: Thus, one deserve to deduce the following identity, assuming \$=n\$​​​​​​​ Source:https://en.wikipedia.org/wiki/Power_set#Relation_to_binomial_theorem comment

← Prev.Next →← Prev. Qn. in Below.Next Qn. in Below. →

## Related questions

1
97 views
Michael Sipser Edition 3 Exercise 0 Question 4 (Page No. 26)If A has a aspects and B has actually b elements, how many aspects are in A × B? Explain your answer.
If A has actually a facets and B has actually b elements, how many kind of elements are in A × B? Exordinary your answer. askedApr 13, 2019in Theory of ComputationLakshman Patel RJIT97 views
2
83 views
Michael Sipser Edition 3 Exercise 0 Inquiry 3 (Page No. 26)Let A be the collection x, y, z and also B be the set x, y. a. Is A a subset of B? b. Is B a subset of A? c. What is A ∪ B? d. What is A ∩ B? e. What is A × B? f. What is the power collection of B?
Let A be the collection x, y, z and also B be the set x, y. a. Is A a subcollection of B? b. Is B a subcollection of A? c. What is A ∪ B? d. What is A ∩ B? e. What is A × B? f. What is the power set of B? askedApr 13, 2019in Theory of ComputationLakshmale Patel RJIT83 views
3
137 views
Michael Sipser Edition 3 Exercise 0 Concern 8 (Page No. 26)Consider the undirected graph G= (V, E) where V , the collection of nodes, is 1, 2, 3, 4 and E, the collection of edges, is 1, 2, 2, 3, 1, 3, 2, 4, 1, 4. Draw the graph G. What are the degrees of each node? Indicate a path from node 3 to node 4 on your drawing of G.
Consider the undirected graph G= (V, E) wbelow V , the collection of nodes, is 1, 2, 3, 4 and E, the set of edges, is 1, 2, 2, 3, 1, 3, 2, 4, 1, 4. Draw the graph G. What are the levels of each node? Indicate a course from node 3 to node 4 on your illustration of G.

See more: How To Change Key Signature In Musescore, Change The Key Signature In The Middle Of A Staff askedApr 13, 2019in Theory of ComputationLakshmale Patel RJIT137 views  