Introduction to Sets

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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 ⁺

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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

From sets to 11th grade math

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