### Sets And Relations Question 2

#### Question 2 - 24 January - Shift 2

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 ________

## Show Answer

#### Answer: 13

#### Solution:

#### Formula: Equivalence relation (vii)

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.