Given to relation `R={(1,2),(2,3)}` on the set `A={1,2,3},` add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

Explanation

Here, `A = {1,2,3}`.

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

To make `R` reflexive, we will add `(1,1),(2,2),(3,3)`.

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

To make `R` symmetric, we will add `(2,1),(3,2),`.

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

To make `R` transitive, we will add `(1,3),(3,1),`.

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