Let `A={1,2,3}` and `R={(1,2),(1,1),(2,3)}` be a relation on `A` . What minimum number of ordered pairs may be added to `R` so that it may become a transitive relation on `Adot`

Explanation

A relation `R` is transitive when

`(a,b) in R and (b,c) in R`,

Then, `(a,c) in R`.

Here,

`R = {(1,2),(1,1),(2,3)}`

Here, we have `(1,2) and (2,3)`, so if we add ordered pair `(1,3)`, `R` will become transitive.

`:. R = {(1,2),(1,1),(2,3),(1,3)}`

Now, `R` is transitive.