a) Define the power set of a set S.________________b) When

Chapter 2, Problem 4RQ

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QUESTION:

Problem 4RQ

a) Define the power set of a set S.

b) When is the empty set in the power set of a set S?

c) How many elements does the power set of a set S with n elements have?

 

Questions & Answers

QUESTION:

Problem 4RQ

a) Define the power set of a set S.

b) When is the empty set in the power set of a set S?

c) How many elements does the power set of a set S with n elements have?

 

ANSWER:

Solution:

 Step 1:

  1. In this problem we need to define the power set of a set S .

            Definition: The power set  of any set S  is the set of all subsets of S , including the empty set and S itself , and it is denoted by .

    Example : S = { a, b , c} .

    .

   If there are n elements in a set  then the power set contains  elements.

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