Let R be the relation in the set {1, 2, 3} gi | vedclass

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(B) relation $R$ on a set $A$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. Reflexive: For every $a \in A$,$(a, a) \in R

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$R$ is an equivalence relation.

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(B) relation $R$ on a set $A$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. Reflexive: For every $a \in A$,$(a, a) \in R$. Here,$(1, 1), (2, 2), (3, 3) \in R$,so it is reflexive.$2$. Symmetric: If $(a, b) \in R$,then $(b, a) \in R$. Since all elements are of the form $(a, a)$,swapping them results in the same pair,so it is symmetric.$3$. Transitive: If $(a, b) \in R$ and $(b, c) \in R$,then $(a, c) \in R$. For this relation,this condition is vacuously satisfied as there are no distinct pairs $(a, b)$ and $(b, c)$ that would require a different $(a, c)$.Since $R$ satisfies all three properties,it is an equivalence relation.

Let $R$ be the relation in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3)\}$. Choose the correct answer.

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