Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

Asked by Pragya Singh | 11 months ago |  99

##### Solution :-

(i) We are provided with the fact that,

A {1,2,3,4,6},R= {(a,b) : a,b ∈ A,bis exactly divisible by a}

Using the conditions given in the problem, we get,

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)}

And this is the roster form of the relation.

(ii)  We are provided with the fact that,

A {1,2,3,4,6}, R= {(a,b) : a,b ∈ A,bis exactly divisible by a}

We can clearly see, the domain of R is, {1,2,3,4,6}

(iii)

We are provided with the fact that,

A {1,2,3,4,6}, R= {(a,b) : a,b ∈ A,bis exactly divisible by a}

And similarly, the range of R is, {1,2,3,4,6}

Answered by Abhisek | 11 months ago

### Related Questions

#### Let R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N

Let R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.

#### Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

#### Let R = {(x, x2) : x is a prime number less than 10}.

Let R = {(x, x2) : x is a prime number less than 10}.

(i) Write R in roster form.

(ii) Find dom (R) and range (R).