Question

Let A = {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by

$R=\left\{\right(a,b):a,bϵA,b$ is exactly divisible by a}

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

Answer 1

We have,

A = {1, 2, 3, 4, 5, 6}

and, R = {(a, b) : a, b \epsilon A, b\) is exactly divisible by a}

(i) Now, $\frac{a}{b}$ stands for 'a divides b'. For the elements of the given sets A and A, we find that

$\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},\frac{2}{2},\frac{2}{4},\frac{2}{6},\frac{3}{3},\frac{3}{6},\frac{4}{4},\frac{5}{5},\frac{6}{6}$

Relatino R in roster form is

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

(ii) Domain (R) = {1, 2, 3, 4, 5, 6}

(iii) Range (R) = {1, 2, 3, 4, 5, 6}