Question

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.

Answer 1

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)}`.