Question

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} 

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

Answer 1

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

x = 2y 

When y = 1 ⇒ x = 2 x 1 = 2 

When y = 2 ⇒ x = 2 x 2 = 4 

When y = 3 ⇒ r = 2 x 3 = 6 

When y = 4 ⇒ x = 2 x 4 = 8

(a) Arrow diagram

(b) Graph

(c) Roster form R = {(2, 1) (4, 3)}

(ii) x = {1, 2, 3, 4, 5, 6, 7, 8, 9} 

y = {1, 2, 3, 4, 5, 6, 7, 8, 9} 

y = x + 3 

When x = 1 ⇒ y = 1 + 3 = 4 

When x = 2 ⇒ y = 2 + 3 = 5 

When x = 3 ⇒ y = 3 + 3 = 6 

When x = 4 ⇒ y = 4 + 3 = 7

When x = 5 ⇒ y = 5 + 3 = 8 

When x = 6 ⇒ y = 6 + 3 = 9 

When x = 7 ⇒ y = 7 + 3 = 10 

When x = 8 ⇒ y = 8 + 3 = 11 

When x = 9 ⇒ y = 9 + 3 = 12 

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

(a) Arrow diagram

(b) Graph​​​​​​​

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