R = {(1,1), (2,2), (3,3)} is defined on the s | vedclass

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(D) The set is $A = \{1, 2, 3\}$.$A$ relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Here,$(1,1), (2,2), (3,3) \in R$,so $R$

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an equivalence relation

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(D) The set is $A = \{1, 2, 3\}$.$A$ relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Here,$(1,1), (2,2), (3,3) \in R$,so $R$ is reflexive.$A$ relation $R$ is symmetric if $(a, b) \in R \implies (b, a) \in R$. Here,all pairs are of the form $(a, a)$,so the condition holds trivially. Thus,$R$ is symmetric.$A$ relation $R$ is transitive if $(a, b) \in R$ and $(b, c) \in R \implies (a, c) \in R$. Here,the condition holds trivially for all elements. Thus,$R$ is transitive.Since $R$ is reflexive,symmetric,and transitive,it is an equivalence relation.Therefore,the correct option is $D$.

$R = \{(1,1), (2,2), (3,3)\}$ is defined on the set $A = \{x : x \in N, x < 4\}$. Then the relation $R$ is . . . . . . .

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