Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on $A imes B$ by $\left(a_{

Question

Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on $A 	imes B$ by $\left(a_{1}, b_{1}ight) R\left(a_{2}, b_{2}ight)$ if and only if $a_{1}+a_{2}=b_{1}+b_{2}$. Then the number of elements in $R$ is $\_\_\_\_$ .\

Professor PC Thomas Classes · Answer

(25) : Given, $A=\{2,3,6,7\}$ and\ $B=\{4,5,6,8\}$\ $\left(a_{1}, b_{1}ight) R\left(a_{2}, b_{2}ight) \Rightarrow a_{1}+a_{2}=b_{1}+b_{2}$\ $\left.\begin{array}{ll}(2,4) R(6,4) & (3,6) R(7,4) \ (2,4) R(7,5) & (3,5) R(7,5) \ (2,5) R(7,4) & (6,5) R(7,8) \ (3,4) R(6,5) & (6,8) R(7,5) \ (3,5) R(6,4) & (7,6) R(7,8) \ (3,4) R(7,6) & (6,4) R(6,8)\end{array}ight] 	imes 2$\ Hence, total number of elements\ $=13 	imes 2-1=25$\