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Chapter 0: Q5E (page 26)

If Cis a set withcelements, how many elements are in the power set of C? Explain your answer.

Short Answer

Expert verified

The number of elements in the power set of Cis2c elements.

Step by step solution

01

Define Power Set

The number of elements in the set Sisn, then its power set consists of2nelements. The Power set is a set of all subsets of a set including empty set.

For example, the power set of set{1,2} is {蠒,{1},{2},{1,2}}.

02

Substitute ‘c’ instead of ‘n’

The set Ccontainsc elements such as{c1,c2,c3,...cc}. By substitutingcinstead ofn,the number of elements in the power set of Cis 2celements.

Therefore, the number of elements in the power set of Cis2c elements.

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