Let R₁ be a relation defined by R₁ = {(a, b)| a $\ge$ b; a, b $\in$ R}. Then R₁ is

For any a $\in$R, we have a $\ge$ a, Therefore the relation R₁ is reflexive but it is not symmetric as (2, 1) $\in$ R₁ but (1, 2) $\notin$ R₁. The relation R₁ is transitive also, because (a, b) $\in$ R₁, (b, c) $\in$ R₁ imply that a $\ge$ b and b $\ge$ c which is turn imply that a $\ge$ c $\Rightarrow$ (a, c) $\in$ R₁.