JEE MAIN - Mathematics (2023 - 30th January Morning Shift - No. 2)
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 :
7
3
4
5
Explanation
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
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