Let $A=\{1,2,3,4, \ldots, 10\}$ and $B=\{0,1,2,3,4\}$. The number of elements in the relation $R=\{(

Question

Let $A=\{1,2,3,4, \ldots, 10\}$ and $B=\{0,1,2,3,4\}$. The number of elements in the relation $R=\{(a, b) \in A 	imes A$ : $\left.2(a-b)^{2}+3(a-b) \in Bight\}$ is

Professor PC Thomas Classes · Answer

(18) : $A=\{1,2,3,4, \ldots \ldots, 10\}$\ $B=\{0,1,2,3,4\}$\ $R=\left\{(a, b) \in A 	imes A: 2(a-b)^{2}+3(a-b) \in Bight\}$\ Now, $2(a-b)^{2}+3(a-b)=(a-b)[2(a-b)$ +3] $\in B$\ $\Rightarrow \quad a=b$ or $a-b=-2$\ When, $a=b \Rightarrow 10$ ordered pairs\ When, $a-b=-2$\ $\Rightarrow \quad 8$ ordered pairs. Total $=18$\