1.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y) : the difference between x and y is odd, x A, y B}. Write R in Roster form.

Answer»

Given, 

Relation R from A to B by R = {(x, y): the difference between x and y is odd, xA, y B} 

A = {1, 2, 3, 5} and B = {4, 6, 9} 

For x = 1 :

y – x = 4 – 1 = 3 which is odd 

⇒ 4 y 

y – x = 6 – 1 = 5 which is odd 

⇒ 6 y 

y – x = 9 – 1 = 8 which is even 

⇒ 8 ∉ y 

For x = 2 :

 y – x = 4 – 2 = 2 which is even 

⇒ 4 ∉ y 

y – x = 6 – 2 = 4 which is even 

⇒ 6 ∉ y y – x = 9 – 2 = 7 which is odd 

⇒ 8 y 

For x = 3 : 

y – x = 4 – 3 = 1 which is odd 

⇒ 4 y 

y – x = 6 – 3 = 3 which is odd 

⇒ 6 y 

y – x = 9 – 3 = 6 which is even 

⇒ 8 ∉ y 

For x = 5 : 

x – y = 5 – 4 = 1 which is odd 

⇒ 4 y 

y – x = 6 – 5 = 4 which is even 

⇒ 6 ∉ y 

y – x = 9 – 4 = 4 which is even 

⇒ 8 ∉ y 

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

NOTE : 

Domain of relation R= {1, 2, 3, 5} 

Range of relation R= {4, 6, 8}


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