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1.Relation and Function
medium
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 $.........$
A
$11$
B
$12$
C
$19$
D
$13$
(JEE MAIN-2023)
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.
Standard 12
Mathematics
