# Introduction to Sets

The concept of sets is important in all branches of modern mathematics. This concept is used in Physics,Chemistry, all Engineering sciences and even in Medical science now-a-days. The mathematician George Cantor has major contribution in introducing and developing the concept of set.A collection of

**well-defined**distinct objects is called a set.

**For example**

1) Collection of all positive even integers is a set. 2 is in this set and 1 is not in this set.

2) The collection of all obese persons in any city is not a set, as there is no definite criteria for obesity.

**Thus, a set is to be understood as a definite collection.**

**Example :**

1) A deck of 52 playing cards.

2) The names of the days of a week.

3) A set of instruments on a geometry box.

The objects of a set are called its

**elements**or

**members.**

If N represents the set of natural numbers . 1,2,3,4,5 ,6,…

So 1,2,3,… are elements of the set

**N.**

Here as 4 is a member of the set A then we write 4 ∈ A and read as 4 belongs to set A or 4 is in an element of set A.

If 0 is not a member of set A then we write 0 ∉ A and read as 0 does not belong to set A.

**Important set in Mathematics**

1) Set of natural numbers = N = { 1,2,3,4,5,…}

2) Set of whole numbers = W = { 0,1,2,3,… }

3) Set of integers = Z = {…, -3,-2,-1,0,1,2,3, … }

4) Set of rational numbers = Q = { 2 / 3 , -5 / 7, -10 / -3,…} . The elements of this set is in p/q form.

5) Set of real numbers = R = { all whole numbers, integers, rational and irrational numbers}

6) Set of all positive numbers = Z

^{+}

**Set Theory**

• Sets

• Representation of-Set

• Cardinal Number

• Types of -Set

• Pairs of -Set

• Subset

• Complement-Set

• Union of the-Set

• Intersection-set

• Operations on-Set

• De Morgan's Law

• Venn Diagrams

• Venn-diagrams for set

• Venn-diagrams for different situations

• Problems on Intersection of Two-Set

• Problems on Intersection three-set

• Sets

• Representation of-Set

• Cardinal Number

• Types of -Set

• Pairs of -Set

• Subset

• Complement-Set

• Union of the-Set

• Intersection-set

• Operations on-Set

• De Morgan's Law

• Venn Diagrams

• Venn-diagrams for set

• Venn-diagrams for different situations

• Problems on Intersection of Two-Set

• Problems on Intersection three-set

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