HOW TO REPRESENT RELATION IN ARROW DIAGRAM

Question 1 :

Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster form, wherever possible.

(i) {(x, y)| x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}

Solution :

Given that :

x = 2y

y = x/2

Hence the required relation is {(2, 1) (3, 3/2) (4, 2) (5, 5/2)}

(i)  Arrow diagram

(ii)  A graph

(iii)  in roster form 

  = {(2, 1) (4, 2)}

(ii) {(x, y) | y = x + 3, x, y are natural numbers < 10}

Solution :

Given that :

y = x + 3

R = {(1, 4) (2, 5) (3, 6) (4, 7) (5, 8) (6, 9)}

An arrow diagram :

(ii)  A graph

In Roster form : 

  =  {(1, 4) (2, 5) (3, 6) (4, 7) (5, 8) (6, 9)}

Question 2 :

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provide ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. If A₁, A₂, A₃, A₄ and A₅ were Assistants; C₁, C₂, C₃, C₄ were Clerks; M₁, M₂, M₃ were managers and E₁, E₂ were Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram.

Solution :

"x" be the salary given to person

"y" be the set of employees

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