Problem 19E
What is the cardinality of each of these sets?
a) {a}
b) {{a}}
c) {a,{a}}
d) {a, {a}, {a. {a}}}
Solution:
Step1
To find
We have to find what is the cardinality of sets?
Step2
The cardinality of a set is a measure of a set’s size, which means the quantity of components in the set. For example, the set B=1,2,4 has a cardinality of 3, for the three components that are in it.
a) {a}
In the given set the quantity of component in the set is one.
Therefore, the cardinality of set is 1.
Step3
b) {{a}}
In the given set the quantity of component in the set is one.
Therefore, the cardinality of set is 1.
Step4
c) {a,{a}}
In the given set the quantity of component in the set is two.
Therefore, the cardinality of set is 2.
Step5
d) {a, {a}, {a. {a}}}
In the given set the quantity of component in the set is three.
Therefore, the cardinality of set is 3.
