The relation R = {(a, a), (b, b), (c, c), (a, | vedclass

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(D) Given the set $A = \{a, b, c\}$ and the relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$.$1$. Reflexivity: For $R$ to be reflexive,$(a, a

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An equivalence relation

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(D) Given the set $A = \{a, b, c\}$ and the relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$.$1$. Reflexivity: For $R$ to be reflexive,$(a, a), (b, b), (c, c)$ must be in $R$. Since all these are present,$R$ is reflexive.$2$. Symmetry: For $R$ to be symmetric,if $(x, y) \in R$,then $(y, x) \in R$. Here,$(a, b) \in R$ and $(b, a) \in R$. Thus,$R$ is symmetric.$3$. Transitivity: For $R$ to be transitive,if $(x, y) \in R$ and $(y, z) \in R$,then $(x, z) \in R$. Here,$(a, b) \in R$ and $(b, a) \in R$,but $(a, a) \in R$. Also $(b, a) \in R$ and $(a, b) \in R$,and $(b, b) \in R$. All conditions are satisfied,so $R$ is transitive.Since $R$ is reflexive,symmetric,and transitive,it is an equivalence relation. The original question provided an incomplete relation; assuming the standard definition for this problem type,the correct classification is an equivalence relation.

The relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$ is defined on the set $A = \{a, b, c\}$. Then $R$ is . . . . . . .

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