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Determine the cardinality of each of the following sets. (a) A = {{}}. (b) B = {, {}}

Chapter 2, Problem 8

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QUESTION:

Determine the cardinality of each of the following sets.

a. \(A=\{\{\emptyset\}\}\).

b. \(B=\{\emptyset,\{\emptyset\}\}\).

c. \(C=\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\}\).

Questions & Answers

QUESTION:

Determine the cardinality of each of the following sets.

a. \(A=\{\{\emptyset\}\}\).

b. \(B=\{\emptyset,\{\emptyset\}\}\).

c. \(C=\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\}\).

ANSWER:

Step 1 of 3

A set is a group of elements. The cardinality of a set is the number of elements in the set. 

(a)

Consider the set \(A=\{\{\emptyset\}\}\). The set has only one element \(\{\emptyset\}\). Thus the cardinality of the set A is 1. We can write it as |A| = 1.

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