Show that relation R in set {1,2,3} given by R ={(1,2),(2,1)} is symmetric but neither reflexive nor

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1.Relation and Function

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Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,2),(2,1)\}$ is symmetric but neither reflexive nor transitive.

Option A

Option B

Option C

Option D

Solution

Let $A=\{1,2,3\}$

A relation $R$ on $A$ is defined as $R =\{(1,2),\,(2,1)\}$

It is clear that $(1,1),\,(2,2),\,(3,3) \notin R$

$\therefore R$ is not reflexive.

Now, as $(1,2)\in R$ and $(2,1)\in R$, then $R$ is symmetric.

Now, $(1,2) $ and $(2,1)\in R$

However, $(1,1)\notin R$

$\therefore R$ is not transitive.

Hence, $R$ is symmetric but neither reflexive nor transitive.

Standard 12

Mathematics

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