- Home
- Standard 12
- Mathematics
Let $R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A= \{3, 5, 9, 12\}.$ Then, $R$ is
reflexive, symmetric but not transitive.
symmetric, transitive but not reflexive.
an equivalence relation.
reflexive, transitive but not symmetric.
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 $aRc$.