LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

__RELATION & MAPPING - REPRESENT 'R' IN THE FORM OF ARROW DIAGRAM & ROSTER FORM__

**Example.1) Let, A = {3, 4, 5, 6}, B = {27, 64, 125, 216}
and R be the relation “is the cube root of” from the set A to set B. Represent
R in the form of a arrow diagram and in the roster form.**

** Ans.) Since, 27 = ^{3}√3, 64 = ^{3}√4, 125 = ^{3}√5 , 216 = ^{3}√6,
from here we can write 3 R 27, 4 R 64, 5 R 125, 6 R 216.**

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**So, the ordered pairs
are (3, 27), (4, 64), (5, 125), and (6, 216). The arrow diagram is shown alongside.**

**In the roster form, R can be written as
follows –**

** R
= {(3, 27), (4, 64), (5, 125), (6, 216)}**

**So, R = {(a, b) : a Є A, b Є B and a = ^{3}√b}**

**Example.2) Let, A = {2,
5, 7, 9}, B = {27, 6, 15, 49} and R be the relation “is a factor of” from A to
set B. Represent R with the help of an arrow diagram and in the roster form.**

**Ans.)
2 is a factor of 6, 5 is a factor
of 15, 7 is a factor of 49, 9 is a factor of 27**

**So, we express the relation like – 2 R
6, 5 R 15, 7 R 49, and 9 R 27**

**So, the ordered pairs are (2, 6), (5,
15), (7, 49), and (9, 27)**

**So, The arrow diagram is shown below –**

**In the Roster form, R can be written as
follows –**

**
R = {(2, 6), (5, 15), (7, 49),
(9, 27)}**

**
R = {(a, b) : a Є A, b Є B and a is the factor of
b}**