Sets, Relations and Function: Consider the following two binary relations on the set A=\a,b,c\ :… | JEE Main 2018

JEE Main 2018 (Online) 15th April Morning ShiftQuestion 1

Consider the following two binary relations on the set $A=\{a,b,c\}$ : $R_1=\{(c,a),(b,b),(a,c),(c,c),(b,c),(a,a)\}$ and $R_2=\{(a,b),(b,a),(c,c),(c,a),(a,a),(b,b),(a,c)\}$. Then

Sets, Relations and Function

$R_2$ is symmetric but it is not transitive✓ Correct answerBoth $R_1$ and $R_2$ are transitiveBoth $R_1$ and $R_2$ are not symmetric$R_1$ is not symmetric but it is transitive

Solution

$R_2$ contains each pair with its reverse, so it is symmetric, but $(c,a),(a,b)\in R_2$ while $(c,b)\notin R_2$, so it is not transitive. ($R_1$ fails both: $(b,c)\in R_1$, $(c,b)\notin R_1$; $(b,c),(c,a)$ but no $(b,a)$.)

Sets, Relations and Function - JEE Mathematics question (JEE Main 2018 (Online) 15th April Morning Shift)

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