Three relation R_2 is defined in set A= a, b, c as follows: R_2= … - Vidyadip

Question

Three relation $R_2$ is defined in set $A=\{a, b, c\}$ as follows:
$R_2=\{(a, a)\}$
Find whether or not the relation $R _2$ on A is:

Reflexive.
Symmetric.
Transitive.

✓

Answer

$R_2$ is Reflexive: Clearly $a, a \in R_2$
Therefore, $R_2$ is reflexive.
Symmetric: Clearly, $a, a \in R \Rightarrow a, a \in R$.
Therefore, $R _2$ is symmetric.
Transitive: $R _2$ is clearly a transitive relation, since there is only one element in it.

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