Question

Let the relation R be defined in $N$ by $aRb$ if $2a+3b=30.$ Then $R=$
.

Answer 1

Find the values of a and b for which given relation satisfied

Given : $aRb:2a+3b=30\&a,b\in N$

$\Rightarrow 3b=30-2a$

$\Rightarrow b=\frac{30-2a}{3}=10-\frac{2a}{3}$

$\Rightarrow a$ must be a multiple of 3

Now,

For $a=3\Rightarrow b=8$

For $a=6,\Rightarrow b=6$

For $a=9,\Rightarrow b=4$

For $a=12,\Rightarrow b=2$

$\therefore$​ The required result is

$R=\{3,8),(6,6),(9,4),(12,2)\}$​​​​​​