Let `R` and `S` be two non-void relations on a set A. Which of the following statements is false?

Options

A. R and S are transitive `implies R uu S` is transitive
B. R and S are transitive implies `R nn S` is symmetric
C. R and S are symmetric implies `R uu S` is symmetric
D. R and S are reflexive implies `R nn S` is reflexive

Answer

A

Explanation

Let A = {1, 2, 3}, R = {(1, 1) (1, 2)}
and S = {(2, 2), (2, 3)} be the transitive relation on A.
Then, `R uu S = {(1, 1), (1, 2), (2, 2), (2, 3)}`
`R uu S` is not transitive, because `(1, 2) in R uu S` and (2, 3) `in R uu S` but (1, 3) `cancelin R uu S`.