Q. 164.6( 5 Votes )

# 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, x A, 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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