# 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

• 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