Question

Let $R=\{(a,a),(b,c),(a,b)\}$ be a relation on a set $A=\{a,b,c\}.$ Then the minimum number of ordered pairs which when added to R make it an equivalence relation are ...

Answer 1

$\{(b,b),(c,c),(b,a),(c,b),(a,c),(c,a)\}$
$R=\{(a,a),(b,c),(a,b)\}$
For relexive add $(b,b),(c,c).$
$\therefore R=\{(a,a),(b,c),(a,b)(b,b)(c,c)(c,b),(b,a)\}(a,b)ϵR(b,c)ϵR$ so that (a,c) must belong to R.
Hence we must add (a,c) and for symmetric we must add (c,a) also.
$\therefore R\{(a,a),(b,c),(a,b)(b,b),(c,c),(c,b),(b,a)(a,c)(c,a)\}$
Ans: 6