Let $A=\{1,2,3, \ldots ., 20\}$. Let $R_{1}$ and $R_{2}$ be two relation on $A$ such that $R_{1}=\{(

Question

Let $A=\{1,2,3, \ldots ., 20\}$. Let $R_{1}$ and $R_{2}$ be two relation on $A$ such that $R_{1}=\{(a, b): b$ is divisible by $a\} R_{2}=\{(a, b): a$ is an integral multiple of $b\}$\ Then, number of elements in $R_{1}-R_{2}$ is equal to $\_\_\_\_$ .\

Professor PC Thomas Classes · Answer

(46) : $R_{1}=\{(1,1),(1,2) \ldots(1,20),(2,2)$, $(2,4), \ldots .(2,20),(3,3),(3,6) \ldots .(3,18),(4,4)$, $(4,8), \ldots .(4,20),(5,5),(5,10),(5,15),(5,20)$, $(6,6),(6,12),(6,18),(7,7),(7,14),(8,8)$, $(8,16),(9,9),(9,18),(10,10),(10,20)$, $(11,11),(12,12),(13,13),(14,14),(15,15)$, $(16,16),(17,17),(18,18),(19,19),(20,20)\} R_{2}=\{(20,1),(20,2),(20,4),(20,5)$, $(20,10),(20,20),(19,19),(19,1),(18,1),(18,2)$, $(18,3),(18,6),(18,9),(18,18),(17,1)$, $(17,17),(16,1),(16,2),(16,4),(16,8)$, $(16,16),(15,1),(15,3),(15,5),(15,15)$, $(14,1),(14,2),(14,7),(14,14),(13,1)$, $(13,13),(12,1),(12,2),(12,3),(12,4)$, $(12,6),(12,12),(11,1),(11,11),(10,1)$, $(10,2),(10,5),(10,10),(9,1),(9,3),(9,9)$, $(8,1),(8,2),(8,4),(8,8),(7,1)(7,7),(6,1)$, $(6,2),(6,3),(6,6),(5,1),(5,5),(4,1),(4,2)$, $(4,4),(3,1),(3,3),(2,1),(2,2),(1,1)\}$\ $R_{1} \cap R_{2}=\{(1,1),(2,2),(3,3),(4,4),(5,5)$, $(6,6),(7,7),(8,8),(9,9),(10,10),(11,11)$, $(12,12),(13,13),(14,14),(15,15),(16,16)$, $(17,17),(18,18),(19,19),(20,20)\}$\ Number of elements in $R_{1}-R_{2}=66-20 =46$ elements.\