If `R` and `S` are transitive relations on a set `A ,` then prove that `RuuS` may not be a transitive relation on `Adot`

Explanation

Let `A={a, b, c}` and `R` and `S` be two relations on `A`, given by


`R={(a, a),(a, b),(b, a),(b, b)}` and


`S={(b, b),(b, c),(c, b),(c, c)}`


Here, the relations `R` and `S` are transitive on `A`.


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


But `(a, c) notin R cup S`


Hence, `R cup S` is not a transitive relation on `A`.