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
if x = 2 y = 2/2 y = 1 |
if x = 3 y = 3/2 |
if x = 4 y = 4/2 y = 2 |
if x = 5 y = 5/2 |
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
if x = 1 y = 4 |
if x = 2 y = 5 |
if x = 3 y = 6 |
if x = 4 y = 7 |
if x = 5 y = 8 |
if x = 6 y = 9 |
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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