Question

Let A = {2, 3, 4, 5, 6). Let R be the relation on A defined by
{(a, b): a ∈ A, b ∈ A, a divides b}. Find :

(i) R

(ii) domain of R

(iii) range of R​

Answer 1

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

R={(a,b):a,b∈A,b is exactly divisible by a}

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

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

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

Answer 2

Given :

• A = {2, 3, 4, 5, 6}
• R be the relation on A defined by
• {(a, b): a ∈ A, b ∈ A, a divides b}

To Find :

1. R = ?
2. Domain of R = ?
3. Range of R = ?

Solution :

1. R :

We have A = {2, 3, 4, 5, 6}.

We observe that :

2/2, 2/4, 2/6, 3/3, 3/6, 4/4, 5/5, 6/6

Hence, 2R2, 2R4, 2R6, 3R3, 3R6, 4R4, 5R5, 6R6

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

2. Domain of R :

Domain of R = {a : (a, b) ∈ R} = {2, 3, 4, 5, 6}.

3. Range of R :

Range of R = {b : (a, b) ∈ R} = {2, 3, 4, 5, 6}.