Mathematics · 2018
JEE Main · 15 April 2018, Shift 1 · Q61
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…
Consider the following two binary relations on the set $\displaystyle \mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ :
$\displaystyle \mathrm{R}_1=\{(\mathrm{c}, \mathrm{a}),(\mathrm{b}, \mathrm{b}),(\mathrm{a}, \mathrm{c}),(\mathrm{c}, \mathrm{c}),(\mathrm{b}, \mathrm{c}),(\mathrm{a}, \mathrm{a})\}$ and $\displaystyle \mathrm{R}_2=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{a}),(\mathrm{c}, \mathrm{c}),(\mathrm{c}, \mathrm{a}),(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{b}),(\mathrm{a}, \mathrm{c})\}$.
Then :
Official answer
(3)
$\displaystyle \mathrm{R}_2$ is symmetric but it is not transitive.
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JEE Main 2018 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.