# Cardinal Number of a Set

What is the cardinal number of a set?

The number of distinct elements in a finite set is called its cardinal number. It is denoted as n(A) and read as ‘the number of elements of the set’.

For example:

(i) Set A = {2, 4, 5, 9, 15} has 5 elements.

Therefore, the cardinal number of set A = 5. So, it is denoted as n(A) = 5.

(ii) Set B = {w, x, y, z} has 4 elements.

Therefore, the cardinal number of set B = 4. So, it is denoted as n(B) = 4.

(iii) Set C = {Florida, New York, California} has 3 elements.

Therefore, the cardinal number of set C = 3. So, it is denoted as n(C) = 3.

(iv) Set D = {3, 3, 5, 6, 7, 7, 9} has 5 element.

Therefore, the cardinal number of set D = 5. So, it is denoted as n(D) = 5.

(v) Set E = {   } has no element.

Therefore, the cardinal number of set D = 0. So, it is denoted as n(D) = 0.

Note:

(i) Cardinal number of an infinite set is not defined.

(ii) Cardinal number of empty set is 0 because it has no element.

Solved examples on Cardinal number of a set:

1. Write the cardinal number of each of the following sets:

(i) X = {letters in the word MALAYALAM}

(ii) Y = {5, 6, 6, 7, 11, 6, 13, 11, 8}

(iii) Z = {natural numbers between 20 and 50, which are divisible by 7}

Solution:

(i) Given, X = {letters in the word MALAYALAM}

Then, X = {M, A, L, Y}

Therefore, cardinal number of set X = 4, i.e., n(X) = 4

(ii) Given, Y = {5, 6, 6, 7, 11, 6, 13, 11, 8}

Then, Y = {5, 6, 7, 11, 13, 8}

Therefore, cardinal number of set Y = 6, i.e., n(Y) = 6

(iii) Given, Z = {natural numbers between 20 and 50, which are divisible by 7}

Then, Z = {21, 28, 35, 42, 49}

Therefore, cardinal number of set Z = 5, i.e., n(Z) = 5

2. Find the cardinal number of a set from each of the following:

(i) P = {x | x ∈ N and x$$^{2}$$ < 30}

(ii) Q = {x | x is a factor of 20}

Solution:

(i) Given, P = {x | x ∈ N and x$$^{2}$$ < 30}

Then, P = {1, 2, 3, 4, 5}

Therefore, cardinal number of set P = 5, i.e., n(P) = 5

(ii) Given, Q = {x | x is a factor of 20}

Then, Q = {1, 2, 4, 5, 10, 20}

Therefore, cardinal number of set Q = 6, i.e., n(Q) = 6

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

## Recent Articles

1. ### 5th Grade Fractions | Definition | Examples | Word Problems |Worksheet

Jul 16, 24 09:33 AM

In 5th Grade Fractions we will discuss about definition of fraction, concept of fractions and different types of examples on fractions. A fraction is a number representing a part of a whole. The whole…

2. ### Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

Jul 16, 24 02:20 AM

In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

3. ### Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

Jul 16, 24 01:36 AM

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

4. ### Worksheet on Add and Subtract Fractions | Word Problems | Fractions

Jul 16, 24 12:17 AM

Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example $$\frac{7}{13}$$ > \(\frac{2…