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 $\text{a, a}\in\text{R}_2$
Therefore, $R_2$ is reflexive.
Symmetric: Clearly, $\text{a, a}\in\text{R}\Rightarrow\ \text{a, a}\in\text{R}.$
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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