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Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on A $\times$ B by $\left(a_1, b_1\right) R\left(a_2, b_2\right)$ is and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $\mathrm{R}$ is ...........
$34$
$25$
$31$
$20$
Solution
$ A=\{2,3,6,7\} $
$ B=\{2,5,6,8\} $
$ \left(a_1, b_1\right) R\left(a_2, b_2\right) $
$ a_1+a_2=b_1+b_2$
$1$. $(2,4) \mathrm{R}(6,4) \quad$ 2. $(2,4) \mathrm{R}(7,5)$
$3$. $(2,5) \mathrm{R}(7,4) \quad$ 4. $(3,4) \mathrm{R}(6,5)$
$5$. $(3,5) \mathrm{R}(6,4) \quad$ 6. $(3,5) \mathrm{R}(7,5)$
$7$. $(3,6) \mathrm{R}(7,4) \quad$ 8. $(3,4) \mathrm{R}(7,6)$ $\times 2$
$9$. $(6,5) \mathrm{R}(7,8) \quad$ 10. $(6,8) \mathrm{R}(7,5)$
$11$. $(7,8) \mathrm{R}(7,6) \quad$ 12. $(6,8) \mathrm{R}(6,4)$
$13$. $(6,6) \mathrm{R}(6,6)$
Total $24+1=25$
