Define a relation R on the set N of natural numbers by R = {(x, y): y�

1.	Define a relation R on the set N of natural numbers by R = {(x, y): y = 2x - 1; x, y ∈ N, x ≤ 5}. Depict this relationship using roster form, Write down the domain and range.
Answer» Given y = 2x – 1 and x ≤ 5 for x = 1, y = 2 × 1 – 1 = 1 x = 2, y = 2 × 2 – 1 = 3 x = 3, y = 2 × 3 – 1 = 5 x = 4, y = 2 × 4 – 1 = 7 x = 5, y = 2 × 5 – 1 = 9 Relation R = {(1, 1), (2, 3), (3, 5), (4, 7), (5, 9)} ∴ Domain = {1, 2, 3, 4, 5} ∴ Range = {1, 3, 5, 7, 9}

Define a relation R on the set N of natural numbers by R = {(x, y): y = 2x - 1; x, y ∈ N, x ≤ 5}. Depict this relationship using roster form, Write down the domain and range.

Answer»

Given y = 2x – 1 and x ≤ 5

for x = 1, y = 2 × 1 – 1 = 1

x = 2, y = 2 × 2 – 1 = 3

x = 3, y = 2 × 3 – 1 = 5

x = 4, y = 2 × 4 – 1 = 7

x = 5, y = 2 × 5 – 1 = 9

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

∴ Domain = {1, 2, 3, 4, 5}

∴ Range = {1, 3, 5, 7, 9}