Set Theory

The set theory was developed by George Cantor in 1845-1918. Today, it is used in almost every branch of mathematics and serves as a fundamental part of present-day mathematics.

In set theory we will learn about representation in roster form and set builder form , types of sets (Empty set, singleton set, finite and infinite sets, equal and equivalent sets), cardinal number of a set, subsets (Proper subset, super set, power set), number of proper subsets, universal set, operation on sets (Union, intersection, difference and complement of sets).

In everyday life, we often talk of the collection of objects such as a bunch of keys, flock of birds, pack of cards, etc. In mathematics, we come across collections like natural numbers, whole numbers, prime and composite numbers. 

Let us examine the following collections:

 Even natural numbers less than 20, i.e., 2, 4, 6, 8, 10, 12, 14, 16, 18. 

 Vowels in the English alphabet, i.e., a, e, i, o, u. 

 Prime factors of 30 i.e. 2, 3, 5. 

 Triangles on the basis of sides, i.e., equilateral, isosceles and scalene. 

We observe that these examples are well-defined collections of objects.

Let us examine some more collections.


Five most renowned scientists of the world.

Seven most beautiful girls in a society.

Three best surgeons in America.

These examples are not well-defined collections of objects because the criterion for determining as most renowned, most beautiful, best, varies from person to person.

Sets:

A set is a well-defined collection of distinct objects.

We assume that,

The word set is synonymous with the word collection, aggregate, class and comprises of elements.

Objects, elements and members of a set are synonymous terms.

Sets are usually denoted by capital letters A, B, C, ....., etc.

Elements of the set are represented by small letters a, b, c, ....., etc.

If ‘a’ is an element of set A, then we say that ‘a’ belongs to A. We denote the phrase ‘belongs to’ by the Greek symbol ‘∈‘ (epsilon). Thus, we say that a ∈ A.

If ‘b’ is an element which does not belong to A, we represent this as b ∉ A.

Some important sets used in mathematics are

N: the set of all natural numbers = {1, 2, 3, 4, .....}

Z: the set of all integers = {....., -3, -2, -1, 0, 1, 2, 3, .....}

Q: the set of all rational numbers

R: the set of all real numbers

Z+: the set of all positive integers

W: the set of all whole numbers

Set Theory

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Complement of a Set

Problems on Operation on Sets

Word Problems on Sets

Venn Diagrams in Different Situations

Relationship in Sets using Venn Diagram

Union of Sets using Venn Diagram

Intersection of Sets using Venn Diagram

Disjoint of Sets using Venn Diagram

Difference of Sets using Venn Diagram

Examples on Venn Diagram






8th Grade Math Practice

From Set Theory to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More