Let ${\mathrm{R}}_1$ be a relation defined by $\mathrm{R\_}1 =\left\{\left(\mathrm{a}, \mathrm{b}\right)\right|\mathrm{a}\ge \mathrm{b}, \mathrm{a}, \mathrm{b}\in \mathrm{R}\}.$ Then ${\mathrm{R}}_1$ is

For any $\mathrm{a}\in \mathrm{R},$ we have $\mathrm{a}\ge \mathrm{a},$ therefore the relation R is reflexive but it is not symmetric as $(2, 1)\in \mathrm{R}$ but 

$(1, 2)\notin \mathrm{R}.$ The relation R is transitive also, because $(\mathrm{a}, \mathrm{b})\in \mathrm{R}, (\mathrm{b}, \mathrm{c})\in \mathrm{R}$ imply that $\mathrm{a}\ge \mathrm{b} \mathrm{and} \mathrm{b}\ge \mathrm{c}$ which is turn imply that $\mathrm{a}\ge \mathrm{c}.$