Question

The minimum number of elements that must be added to the relation $R=\left\{\right(1,2\left)\right(2,3\left)\right\}$ on the set of natural numbers so that it is an equivalence is:

• A. $4$
• B. $7$
• C. $6$
• D. $5$

Answer 1

The correct option is C $6$

Relation $R$ contains
$R=\left\{\right(1,2\left)\right(2,3),(1,1),(2,2),(3,3),(2,1),(3,2),(1,3\left)\right\}$
Total number of elements is $8$ then the number of minimum elements added is $6.$