Question

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.

Answer 1

Here, `A = {a,b,c}.`
`R = {(a,a),(b,c),(a,b)}`
Now, to make `R` reflexive, we should add `(b,b),(c,c)`.
`:. R = {(a,a),(b,c),(a,b),(a,a),(b,b)}.`
Now, `R` is reflexive.
Now, `R` contains `(a,b),(b,c)`, but do not have `(a,c)`.
So, we have to add `(a,c)` to make `R` transitive.
`:. R = {(a,a),(b,c),(a,b),(a,a),(b,b),(a,c)}.`
Now, `R` is transitive and reflexive.