Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A imes A$ defined by $R=\{((a, b),(c, d)): 2

Question

Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A 	imes A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $R$ is

Professor PC Thomas Classes · Answer

(6) : $A=\{1,2,3,4\}$\ $A 	imes A=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3)$, $(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2)$, $(4,3),(4,4)\}$\ $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$\ On checking the elements of $A 	imes A$, we get $\{((1,4),(1,2)),((2,3),(2,1)),((3,1),(1,1))$ $,((3,4),(2,2)),((4,2),(1,2)),((4,3),(3,1))\}$ will satisfy $R$.\ $	herefore \quad$ Number of elements in $R$ is 6 .\