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.