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# What is the cardinality of each of these sets?a) ISBN: 9780073383095 37

## Solution for problem 19E Chapter 2.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 19E

What is the cardinality of each of these sets?

a) {a}

b) {{a}}

c) {a,{a}}

d) {a, {a}, {a. {a}}}

Step-by-Step Solution:
Step 1 of 3

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.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

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What is the cardinality of each of these sets?a)