Let `A={a , b , c)` and the relation R be defined on A as follows: `R={(a , a),(b , c),(a , b)}dot` Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.

Explanation

Given the relation the relation `R` be defined on `A` as follows `R= \{(\{a}, \{a}),(\{b}, \{c}),(\{a}, \{b})\}.`



Now, to make this relation `\{R}` to be reflexive we are to add the elements like `(x, x)` for all x `\in` `A`.



The the relation will be `R=\{(a, a),(b, b),(c, c),(b, c),(a, b)\}`.



Now this relation is reflexive but not transitive as `(a, b) \in A,(b, c) \in A \Rightarrow(a, c) \in A`.



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