The relation R in the set 1,2,3 given by R= (1,2), (2,1),(1,1) is - Vidyadip

MCQ

The relation $R$ in the set $\{1,2,3\}$ given by $R=\{(1,2)$, $(2,1),(1,1)\}$ is

A
symmetric and transitive, but not reflexive
B
reflexive and symmetric, but not transitive
C
symmetric, but neither reflexive nor transitive
D
an equivalence relation

✓

Answer

Given, $R=\{(1,2),(2,1),(1,1)\}$ is a relation on set $\{1,2,3\}$
Reflexive : Clearly $(2,2),(3,3) \notin R$
$\therefore \quad R$ is not a reflexive relation.
Symmetric: Now, $(1,2) \in R$ and $(2,1) \in R \therefore R$ is symmetric.
Transitive: Now, $(2,1) \in R$ and $(1,2) \in R$ but $(2,2) \notin R$
$\therefore \quad R$ is not transitive relation.
$R$ is symmetric, but neither reflexive nor transitive.

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