Let A = \ 2, 3, 4\ and B = \ 8, 9, 12\ . Then the number of...

Given,

A = $\left\{2, 3, 4\right\}$, B = \left\{8, 9, 12\right\}$</p><p>And${a}_{1} \in A, {b}_{2} \in B$</p><p>Now finding elements where${a}_{1}$divides${b}_{2}$we get,</p><p>\left({a}_{1}, {b}_{2}\right)$ \in \left\{\left(2, 8\right), \left(2, 12\right), \left(3, 9\right)$, \left(3, 12\right)$, \left(4, 8\right)$, \left(4, 12\right)</p><p>Also given,${a}_{2} \in A, {b}_{1} \in B$</p><p>Now finding elements when${a}_{2}$divides${b}_{1}$, we get,</p><p>\left({a}_{2}, {b}_{1}\right)$ \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\}$</p><p>Hence, Number of relations$= 6 \times 6 = 36