- Home
- Standard 12
- Mathematics
1.Relation and Function
medium
Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = {1, 2, 3}$, the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is
A
$5$
B
$6$
C
$7$
D
$8$
Solution
(c) $R$ is reflexive if it contains $(1, 1), (2, 2), (3, 3)$
$(1,\,2)\,\, \in R,\,(2,\,3) \in R$
$\therefore $ $R$ is symmetric if $(2, 1), (3, 2) \in R.$
Now, $R = \{ (1,\,1),\,(2,\,2),\,(3,\,3),\,(2,\,1),\,(3,\,2),\,(2,\,3),\,(1,\,2)\} $
$R$ will be transitive if $(3, 1); (1, 3)$ $\therefore$ $R$.
Thus, $R$ becomes an equivalence relation by adding $(1, 1) \,(2, 2)\, (3, 3)\, (2, 1)\, (3,2)\, (1, 3)\, (3, 1)$.
Hence, the total number of ordered pairs is $7$.
Standard 12
Mathematics
