The minimum number of elements that must be added to the relation R = ( a , b ) , ( b , c ) on the set { a ,…

Given:

$A=\left\{a,b,c,d\right\}$

And,

$R=\left\{\left(a,b\right),\left(b,c\right)\right\}$

For symmetric relation, we must add $\left(b,a\right), \left(c,b\right)$.

So, $R=\left\{\left(a,b\right),\left(b,a\right), \left(b,c\right),\left(c,b\right)\right\}$.

For transitive relation, we must add

$\left(a,c\right), \left(b,b\right), \left(c,a\right), \left(a,a\right), \left(c,c\right)$

Hence, 

$R=\left\{\left(b,a\right), \left(c,b\right), \left(a,c\right), \left(b,b\right), \left(c,a\right), \left(a,a\right), \left(c,c\right), \left(a,b\right), \left(b,c\right)\right\}$

So, number of new elements added$=7$