Question

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

• A. $4$
• B. $7$
• C. $6$
• D. $5$

Answer 1

Answer: (B)

$7$

for equivalence relation R
$(a,a)\in R$
if $(a,b)\in R$
then $(b,a)\in R$
if $(a,b)\in R$
$(b,c)\in R$
then $(a,c)\in R$
$R=(1,2),(2,3),(1,1),(2,2),(3,3),(2,1),(3,2),(1,3),(3,1)$
No of added ordered pairs $=9-2=7$