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  4. Let A = 1,2,3 and R = (1,2),(2,3) be a relation in A. Then, the minimum number of ordered pairs may be added, so that R becomes an equivalence relation, is

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Q. Let $A =\{1,2,3\}$ and $R =\{(1,2),(2,3)\}$ be a relation in $A$. Then, the minimum number of ordered pairs may be added, so that $R$ becomes an equivalence relation, is

Relations and Functions - Part 2

Solution:

The given relation is $R =\{(1,2),(2,3)\}$
in the set $A =\{1,2,3\}$
Now, $R$ is reflexive, $if (1,1),(2,2),(3,3) \in R$
$R$ is symmetric, $if (2,1),(3,2) \in R$
R is transitive, if $(1,3)$ and $(3,1) \in R$.
Thus, the minimum number of ordered pairs which are to be added,
so that $R$ becomes an equivalence relation, is $7$ .