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 :
JEE · Math · previous-year question
- A.7correct
- B.3
- C.4
- D.5
Answer
A. 7
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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