Solution Found!
Determine the cardinality of each of the following sets. (a) A = {{}}. (b) B = {, {}}
Chapter 2, Problem 8(choose chapter or problem)
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.