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Q.
Let $R$ be the relation in the set $\{1,2,3,4\}$ given by $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$. Choose the correct answer.
Relations and Functions - Part 2
Solution:
Here, $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$
Since, $(a, a) \in R$., for every $a \in\{1,2,3,4\}$. Therefore, $R$ is reflexive.
Now, since $(1,2) \in R$ but $(2,1) \notin R$. Therefore, $R$ is not symmetric.
Also, it is observed that $(a, b),(b, c) \in R$
$\Rightarrow(a, c) \in R$. For all $a, b, c \in\{1,2,3,4\}$
Therefore, $R$ is transitive. Hence, $R$ is reflexive and transitive but not symmetric.