# 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.

## Recent Articles

1. ### Fundamental Geometrical Concepts | Point | Line | Properties of Lines

Apr 18, 24 02:58 AM

The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

2. ### What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

Apr 18, 24 02:15 AM

What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

3. ### Simple Closed Curves | Types of Closed Curves | Collection of Curves

Apr 18, 24 01:36 AM

In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

4. ### Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

Apr 18, 24 12:31 AM

Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…