Relation in Math

The concept of relation in math refers to an association of two objects or two variables based some property possessed by them.

For Example:

1. Rachel is the daughter of Noah. 

This statement shows the relation between two persons. 

The relation (R) being ‘is daughter of’. 


2. 5 is less than 9. 

This statement shows the relation between two numbers. 

The relation (R) being ‘is less than’. 

If A and B are two non-empty sets, then the relation R from A to B is a subset of A x B, i.e., R ⊆ A x B. 

If (a, b) ∈ R, then we write a R b and is read as 'a' related to 'b'. 



3. Let A and B denote the set animals and their young ones. 

Clearly, A = {cat, dog, cow, goat}

B = {kitten, puppy, calf, kid}

The relation (R) being ‘is young one of ‘.

Then the fact that,

Kitten is the young one of a cat.

Thus, kitten is related to cat.

Puppy is the young one of a dog.

Thus, puppy is related to dog.


Calf is the young one of a cow.

Thus, calf is related to cow.


Kid is the young one of a goat.

Thus, kid is related to goat.


This fact can also be written as set R or ordered pairs.

R = {(kitten, cat), (puppy, dog), (calf, cow), (kid, goat)}

Clearly, R ⊆ B × A

Thus, if A and B are two non-empty sets, then the relation R from A to B is a subset of A×B, i.e., R ⊆ A × B.

If (a, b) ∈ R, then we write a R b and is read as a is related to b.


Representation of Relation in Math:

The relation in math from set A to set B is expressed in different forms. 

      (i) Roster form 

      (ii) Set builder form 

      (iii) Arrow diagram 





i. Roster form: 

● In this, the relation (R) from set A to B is represented as a set of ordered pairs.

● In each ordered pair 1st component is from A; 2nd component is from B.

● Keep in mind the relation we are dealing with. (>, < etc.)

For Example:

1. If A = {p, q, r} B = {3, 4, 5}

then R = {(p, 3), (q, 4), (r, 5)}

Hence, R ⊆ A × B


2. Given A = {3, 4, 7, 10} B = {5, 2, 8, 1} then the relation R from A to B is defined as ‘is less than’ and can be represented in the roster form as R = {(3, 5) (3, 8) (4, 5), (4, 8), (7, 8)}

Here, 1ˢᵗ component < 2ⁿᵈ component.

In roster form, the relation is represented by the set of all ordered pairs belonging to R.

If A = {-1, 1, 2} and B = {1, 4, 9, 10}

if a R b means a² = b

then, R (in roster form) = {(-1, 1), (1, 1), (2, 4)



ii. Set builder form:

In this form, the relation R from set A to set B is represented as R = {(a, b): a ∈ A, b ∈ B, a...b}, the blank space is replaced by the rule which associates a and b.

For Example:

Let A = {2, 4, 5, 6, 8} and B = {4, 6, 8, 9}

Let R = {(2, 4), (4, 6), (6, 8), (8, 10) then R in the set builder form, it can be written as

R = {a, b} : a ∈ A, b ∈ B, a is 2 less than b}


iii. Arrow diagram:

● Draw two circles representing Set A and Set B.

● Write their elements in the corresponding sets, i.e., elements of Set A in circle A and elements of Set B in circle B.

● Draw arrows from A to B which satisfy the relation and indicate the ordered pairs.

Arrow diagram

For Example:



1. If A = {3, 4, 5} B = {2, 4, 6, 9, 15, 16, 25}, then relation R from A to B is defined as ‘is a positive square root of’ and can be represented by the arrow diagram as shown.
Here R = {(3, 9); (4, 16); (5, 25)}





In this form, the relation R from set A to set B is represented by drawing arrows from 1ˢᵗ component to 2ⁿᵈ components of all ordered pairs which belong to R.

Representation of Relation in Math






2. If A = {2, 3, 4, 5} and B = {1, 3, 5} and R be the relation 'is less than' from A to B,
then R = {(2, 3), (2, 5), (3, 5), (4, 5)}







 Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Relation

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function


 Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping









7th Grade Math Problems

8th Grade Math Practice

From Relation in Math to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  2. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  3. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  4. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More

  5. Worksheet on Multiplying 1-Digit Numbers |Multiplying One Digit Number

    Mar 25, 24 03:39 PM

    Multiplication tables will help us to solve the worksheet on multiplying 1-digit numbers. The questions are based on multiplying one digit number and word problems on multiplying one digit number.

    Read More