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  4. On set A = 1, 2, 3, relations R and S are given by R = (1, 1), (2, 2), (3, 3), (1, 2), (2, 1) S = (1, 1), (2, 2), (3, 3), (1, 3), (3, 1) Then

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Q. On set $A = {1, 2, 3}$, relations $R$ and $S$ are given by
$R = \left\{\left(1, 1\right), \left(2, 2\right), \left(3, 3\right), \left(1, 2\right), \left(2, 1\right)\right\}$
$S =\left\{ \left(1, 1\right), \left(2, 2\right), \left(3, 3\right), \left(1, 3\right), \left(3, 1\right)\right\}$ Then

WBJEEWBJEE 2017Relations and Functions - Part 2

Solution:

We have,
$R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\},$
$S=\{(1,1),(2,2),(3,3),(1,3),(3,1)\}.$
$\therefore R \cup S=\{(1,1),(2,2),(3,3),(1,2), (2,1),(1,3),(3,1)\} .$
Since, $(2,1) \in R \cup S,(1,3) \in R \cup S$
but $(2,3) \notin R \cup S$
$\therefore R \cup S$ is reflexive and symmetric but not transitive.