Let A = 2 , 3 , 4 and B = 8 , 9 , 12 . Then the number of elements in the relation R = a 1 , b 1 , a 2 , b 2…

Given,

$A=\left\{2,3,4\right\}, B=\left\{8,9,12\right\}$

And $a_1\in A, b_2\in B$

Now finding elements where $a_1$ divides $b_2$ we get,

$\left(a_1,b_2\right)\in \left\{\left(2,8\right),\left(2,12\right),\left(3,9\right),\left(3,12\right),\left(4,8\right),\left(4,12\right)\right\}$

Also given, $a_2\in A,b_1\in B$

Now finding elements when $a_2$ divides $b_1$, we get,

$\left(a_2,b_1\right)\in \left\{\left(2,8\right),\left(2,12\right),\left(3,9\right),\left(3,12\right),\left(4,8\right),\left(4,12\right)\right\}$

Hence, Number of relations $= 6 \times 6 = 36$