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1.Relation and Function
medium
The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is
A
$0$
B
$1$
C
$2$
D
$3$
(JEE MAIN-2023)
Solution
$A =\{1,2,3\}$
For Reflexive $(1,1)(2,2),(3,3) \in R$
For transitive : $(1,2)$ and $(2,3) \in R \Rightarrow(1,3) \in R$
Not symmetric : $(2,1)$ and $(3,2) \notin R$
$R _1=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$
$R _2=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(2,1)\}$
$R _3=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(3,2)\}$
Standard 12
Mathematics
