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 make it an equivalence relation are...........

Answer 1

$(b,b),(c,c),(b,a),(c,b),(a,c),(c,a)$

$R=(a,b),(b,c),(a,b)$

For reflexive add (b, b), (c, c) .

$\therefore$ $R=(a,a),(b,c),(a,b),(b,b),(c,c)$

For symmetric add $(c,b)$ and $(b,a)$

$\therefore R=(a,a),(b,c)(a,b),(b,b)(c,c),(c,b),(b,a)$

(a, b)$\in$ R, (b, c)$\in$ R so that (a, c) must belong to R.

Hence we must add (a, c) and for symmetric we must add (c, a) also.

$\therefore R=(a,a),(b,c),(a,b),(b,b),(c,c),(c,b),(b,a),(a,c),(c,a)$