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  4. 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

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Q. 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 _______

JEE MainJEE Main 2023Relations and Functions - Part 2

Solution:

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.