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

Question

The minimum number of elements that must be added to the relation $$ \mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$$ on the set $$\{a, b, c\}$$ so that it becomes symmetric and transitive is :

Accepted Answer

For symmetric $$(b,a),(c,b)\in R$$

For transitive $$(a,c)\in R$$

$$\Rightarrow (c,a)\in R$$

$$\therefore (a,b),(b,a)\in R$$

$$\Rightarrow (a,a)\in R$$

$$(b,c),(c,b)\in R$$

$$\Rightarrow (b,b)\in R,(c,c)\in R$$

7 elements must be added

Solutions · 1