Question

Let A= {1,2,3,6,9,18}, find the set R such that R={ (a,b) : a,b ∈ A and divides a and b}

Answer 1

SOLUTION

GIVEN

• Let A= {1,2,3,6,9,18}

• A relation R such that R={ (a,b) : a,b ∈ A and a divides b}

TO DETERMINE

The Set R

EVALUATION

Here it is given that A = { 1 , 2 , 3 , 6 , 9 , 18 }

A relation R such that

R = { (a,b) : a,b ∈ A and a divides b}

Now

$\sf{ \: 1 \: divides \: 1 \: \implies \: (1,1) \: \in R}$

$\sf{ \: 1 \: divides \: 2 \: \implies \: (1,2) \: \in R}$

$\sf{ \: 1 \: divides \: 3 \: \implies \: (1,3) \: \in R}$

$\sf{ \: 1 \: divides \: 6 \: \implies \: (1,6) \: \in R}$

$\sf{ \: 1 \: divides \: 9 \: \implies \: (1,9) \: \in R}$

$\sf{ \: 1 \: divides \: 18 \: \implies \: (1,18) \: \in R}$

$\sf{ \: 2 \: divides \: 2 \: \implies \: (2,2) \: \in R}$

$\sf{ \: 2 \: divides \: 6 \: \implies \: (2,6) \: \in R}$

$\sf{ \: 2 \: divides \: 18 \: \implies \: (2,18) \: \in R}$

$\sf{ \: 3 \: divides \: 3 \: \implies \: (3,3) \: \in R}$

$\sf{ \: 3 \: divides \: 6 \: \implies \: (3,6) \: \in R}$

$\sf{ \: 3 \: divides \: 9 \: \implies \: (3,9) \: \in R}$

$\sf{ \: 3 \: divides \: 18 \: \implies \: (3,18) \: \in R}$

$\sf{ \: 6 \: divides \: 6 \: \implies \: (6,6) \: \in R}$

$\sf{ \: 6 \: divides \: 18 \: \implies \: (6,18) \: \in R}$

$\sf{ \: 9 \: divides \: 9 \: \implies \: (9,9) \: \in R}$

$\sf{ \: 9 \: divides \: 18 \: \implies \: (9,18) \: \in R}$

$\sf{ \: 18 \: divides \: 18 \: \implies \: (18,18) \: \in R}$

Hence the required Set is

R = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 6 ) , ( 1 , 9 ) , ( 1 , 18 ) , ( 2 , 2 ) , ( 2 , 6 ) ,( 2 , 18 ) , ( 3 , 3 ), ( 3 , 6 ) , ( 3 , 9 ) , ( 3 , 18 ) , ( 6 , 6 ) , ( 6 , 18 ), ( 9 , 9 ) , ( 9 , 18 ) , ( 18 , 18 ) }

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