Operations On Sets

In the present day of mathematics sets serves as a fundamental part. Sets are used in every part of mathematics. The theory of the set was given by a German mathematician, and his name is George Cantor. In simple language, let us understand the concept of sets and operation on sets. Suppose we are talking about a pack of cards, a cricket team, or a crowd of people, and in mathematical language, we will take the example as natural numbers, prime numbers, or whole numbers. In the sets, we will arrange all quantities in a well-defined group or collection. There are 5 types of sets which are union sets, the intersection of sets, etc.

Operation on sets

The operation of sets is performed to obtain a certain combination of elements, and sets include three major operations performed on sets like-

● Union sets.

● Intersection sets.

● Difference sets.

Union sets

Assume that there are two sets, namely A and B; then there will be a certain amount of elements in A and the same in B; then, the union of set A and B will be called all the elements which are present in set A and set B, and it is denoted by “U”.

If set A= {1,2,3,4,5,} and set B= {6,7,8,}

Then the union of set A and set B will be, 

A U B = {1,2,3,4,5,6,7,8,}

Intersection of sets

The intersection of sets means that in the two sets A and B if they intersect each other, the values taken will be common in both A&B, and it is denoted by “.

If set A ={1,2,3,4,5} and set B ={4,5,6,7,}

Send the intersection of set and set B will be, 

A B = {4,5}

Difference sets

Difference sets mean that suppose there are two sets A&B and the difference between these two sets will include the elements of only set a but not of set B; we can even refer to different sets as the intersection of set A and the complement of set B.

Complement of a set

In a complement of a set, you will get every set or universal set which are not present in a particular given set; for example, if there is set A and it contains coins and nodes, the universal set of coins and notes will be noted, but it does not include coins.

Cartesian product 

The Cartesian product of sets means that the product of two sets A&B will contain every possible pair of the elements which exist in set A and set B, for example, if there are two sets A and B.

A = {1,2,3,} and B = {4,5}

The cartesian product of these two sets will be,

A x B = {1,4}, {1,5}, {2,4}, {2,5}, {3,4}, {3,5}. This will be the cartesian product of set A and B, and it will include all possible pairs of elements which exist in set A and set B.

Types of sets

There are mainly two types of sets which are- roster form and set builder form.

Roster form

In a roaster or tabular form, the elements are listed, and each element is separated by commas at the starting and the end; these are enclosed with the help of braces.

The important points of roster forms are:

● The roster form is also known as the enumeration form.

● For an empty or for a null set, the roster form is represented by ∅.

● The roster notation is not used for too much data.

Set builder form

In set-builder form, every element has something in common, like whole numbers or natural numbers, and these sets are denoted by “V.”

Symbols Used in set-builder form are mentioned below:-