# Cardinal Number

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