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

Let $\mathrm{A}=\left\{1, 2, 3\right\}$ and $\mathrm{R}=\left\{\left(1, 1\right), \left(1, 2\right)\right\}, \mathrm{S}=\left\{\left(2, 2\right)\left(2, 3\right)\right\}$

be transitive relations on A.

Then $\mathrm{R}\cup \mathrm{S}=\left\{\left(1, 1\right); \left(1, 2\right); \left(2, 2\right); \left(2, 3\right)\right\}$

Obviously, $\mathrm{R}\cup \mathrm{S}$is not transitive. Since $\left(1, 2\right)\in \mathrm{R}\cup \mathrm{S} \mathrm{and} \left(2, 3\right)\in \mathrm{R}\cup \mathrm{S} \mathrm{but} \left(1, 3\right)\notin \mathrm{R}\cup \mathrm{S}.$