1.Relation and Function
hard

જો  $R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ એ ગણ $A= \{3, 5, 9, 12\}.$ પરનો સંબધ હોય તો $R$ એ . . . . 

A

સ્વવાચક અને  સંમિત છે પરંતુ પરંપરિત નથી.

B

 સંમિત અને પરંપરિત છે પરંતુ સ્વવાચક નથી.

C

સામ્ય સંબધ છે .

D

સ્વવાચક અને  પરંપરિત છે પરંતુ સંમિત  નથી.

(JEE MAIN-2013)

Solution

Let $R = \left\{ {\left( {3,3} \right),\left( {5,5} \right),\left( {9,9} \right),\left( {12,12} \right),\left( {5,12} \right),\left( {3,9} \right),\left( {3,12} \right),\left( {3,5} \right)} \right\}$ be arelation on set

$A = \left\{ {3,5,9,12} \right\}$

Clearly, every element of $A$ is related to it self.

Therefore, it is a reflaxive.

Now, $R$ is not syminetry because $3$ is related to $5$ but $5$ is related to $3$.

Also $R$ is transitive relation because it satisfies the property that if $aRb$ and $bRc$ then $aRc$.

 

Standard 12
Mathematics

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