Question

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

• A. 7
• B. 5
• C. 1
• D. 4

Answer 1

Answer: (A)

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 $7$ .