## Set Theory

Set theory is one of the branches of mathematics which plays a vital role in all branches of math.

In set-theory we are going to study about the definition of a set, representation of set, types of sets, and cardinal number of a set. We also learn about subsets, and operations of sets in set-theory.

Also, we will see about Venn diagrams and how Venn diagrams are used to solve word problems in the set.

Definition:

A set is a well defined collection of individual objects (elements).

In our daily life we often refer collection of things, namely a group of keys, pack of cards, a group of people etc.

In math we come across a collection of natural numbers, whole numbers, rational numbers and so on.

For example consider the following collections:

• Five famous surgeons in India
• Top ten business men in world
• Natural numbers less than 10
• Divisors of 20 {1,2,4,5,10,20}

• Sets are usually denoted by capital letters, A, B, C,...
• Elements of sets are denotes small letters, a, b, c, ...

• If an element x of a set A, we say that 'x' belongs to A. We denote the phrase 'belongs' by the symbol (Greek)'∈'. Mathematically a element of a set represented as x∈A.
• If 'a' is an element which does not belong to a set B, then we denote that mathematically as a ∉ B

Some more examples of Sets:

Examples of sets Meaning
A = {f,g,w,u,x,z} A = The set of vowels in the word.
B = {2,7,9,12} B = The set of even numbers between 2 and 10 both inclusive
C = {abr, chu, ops, ngh, pji} C = The set of all possible arrangements of the letters g, h and r.
D = {4,7,9,1,0} D = The set of odd digits between 1 and 9
E = {2,7} E = The set of roots of the equation x2-5x +7.

This type of representation is known as Roaster form or Braces form. In this way, we are making the elements list of the set and we keep them in braces.

Related Topics
• Representation of Set
• types of set
• Disjoint sets
• Power Set
• Operations on Sets
• Laws on set operations
• More Laws
• Venn diagrams
• Set word problems
• Relations and functions

• Set theory Next page

### Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are: