Question

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.

Answer 1

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

(i)

The roaster form of A is given by,

R= b a { ( a,b ):a,b∈A }

Here b must be exactly divisible by a.

The roaster form of A is given by,

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)

The domain of R is given by,

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

(iii)

The range of R is given by,

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