The minimum number of elements that must be added to the relation R...

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)$</p><p>Hence, </p><p>$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\}$</p><p>So, number of new elements added$= 7$