Given the relation R = {(1, 2), (2, 3)} on th | vedclass

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(c) $R$ is reflexive if it contains $(1, 1), (2, 2), (3, 3)$

$(1,\,2)\,\, \in R,\,(2,\,3) \in R$

$	herefore $ $R$ is symmetric if $(2, 1), (3,

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(c) $R$ is reflexive if it contains $(1, 1), (2, 2), (3, 3)$

$(1,\,2)\,\, \in R,\,(2,\,3) \in R$

$	herefore $ $R$ 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 $(3, 1); (1, 3)$ $	herefore$  $R$.

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 $7$.

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

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