# Cardinal Number

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

The cardinal number of set V is the number of distinct element in it and is denoted by n(V).

For example

The vowels in the word DIFFERENTIATE are I, E, E, I, A and E. If we represent the set of vowels in the word DIFFERENTIATE in roster form we have :

P = { I, E, A}

Thus, even thought there are 6 vowels in the word, there are only 3 distinct elements in the set V.

So, cardinal-number n(P) = 3.

Examples :

1) What is the cardinal-number of set A of the composite numbers between 10 and 20?

Solution :
A = { 12,14,15,16,18}

As there are 5 elements in set A.

n(A) = 5.

2) If set C = { x | x is neither a prime nor a composite number}.Find n(C)

Solution :
C = { x | x is neither a prime nor a composite number}

C = {1}

∴ n(C) = 1

3) If J = { 101, 103, 105,107,109}. Find n(J).

Solution :
J = { 101, 103, 105,107,109}

n(J) = 5

4) If B ={ x| x is a letter in the word PENINSULA}. Find n(B).

Solution :
B ={ x| x is a letter in the word PENINSULA}

B = { P, E, N, I, S, U, L, A}

n(B) = 8

5) If E = { a,f,k,p,u,z }. Find n(E).

solution :
E = { a,f,k,p,u,z }

n(E) = 6

6) If Q= { x| 3 < x < 4}. Find n(Q).

Solution :
Q= { x| x ∉ N3 < x < 4}

As there is no element between 3 and 4.

n(Q) = 0

n(Q) = Φ

Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets
Problems on Intersection of Three Sets