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
● Subset
7th Grade Math Problems
From Cardinal Number of a Set to HOME PAGE
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.

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