Given the relation R = {(1, 2), (2, 3)} on th | vedclass

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(C) An equivalence relation must be reflexive,symmetric,and transitive.$1$. Reflexivity: For $R$ to be reflexive on $A = \{1, 2, 3\}$,it must contain

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$7$

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(C) An equivalence relation must be reflexive,symmetric,and transitive.$1$. Reflexivity: For $R$ to be reflexive on $A = \{1, 2, 3\}$,it must contain $(1, 1), (2, 2), (3, 3)$. Since these are not in $R$,we must add $3$ pairs.$2$. Symmetry: Given $(1, 2) \in R$,we must add $(2, 1)$. Given $(2, 3) \in R$,we must add $(3, 2)$.$3$. Transitivity: Given $(1, 2) \in R$ and $(2, 3) \in R$,we must add $(1, 3)$ for transitivity. Since $(1, 3) \in R$,by symmetry,we must also add $(3, 1)$.Combining these,the set of added pairs is $\{(1, 1), (2, 2), (3, 3), (2, 1), (3, 2), (1, 3), (3, 1)\}$.The total number of ordered pairs to be added is $7$.

Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = \{1, 2, 3\}$,the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is

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