Question

The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c),(b,d)\}$ on the set $\{a,b,c,d\}$ so that it is an equivalence relation, is _______

Answer 1

Answer: 13

Given $R=\{(a,b),(b,c),(b,d)\}$
In order to make it equivalence relation as per given set, $R$ must be
$\{(a,a),(b,b),(c,c),(d,d),(a,b),(b,a),(b,c),(c,b)$,
$(b,d),(d,b),(a,c),(a,d),(c,d),(d,c),(c,a),(d,a)\}$
There already given so 13 more to be added.