For a set A = {1, 2, 3},a relation R = {(1, 2 | vedclass

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(C) relation $R$ on set $A$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. For reflexivity,$R$ must contain $(1, 1), (2,

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$7$

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(C) relation $R$ on set $A$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. For reflexivity,$R$ must contain $(1, 1), (2, 2), (3, 3)$.$2$. Given $R = \{(1, 2), (2, 3)\}$.$3$. For symmetry,since $(1, 2) \in R$,we must add $(2, 1)$. Since $(2, 3) \in R$,we must add $(3, 2)$.$4$. Now,$R = \{(1, 2), (2, 3), (2, 1), (3, 2), (1, 1), (2, 2), (3, 3)\}$.$5$. For transitivity,since $(1, 2) \in R$ and $(2, 3) \in R$,we must have $(1, 3) \in R$. For symmetry,we must also add $(3, 1)$.$6$. The final set $R$ becomes the universal relation on $A$,which is $A 	imes A = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)\}$.$7$. The original relation had $2$ elements. The universal relation has $3^2 = 9$ elements.$8$. Number of elements to be added = $9 - 2 = 7$.

For a set $A = \{1, 2, 3\}$,a relation $R = \{(1, 2), (2, 3)\}$ is defined. What is the minimum number of ordered pairs that must be added to $R$ to make it an equivalence relation?

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