Show that the relation "`ge`" on the set `R` of all real numbers is reflexive and transitive but not symmetric.

Explanation

Let us denote the relation `\geq` on the set of real numbers `\mathbb{R}` be `R=\{(a, b): a, b \in \mathbb{R}, a \geq b}`.



Then this relation `R` is reflexive as `a \geq a, \forall a \in \mathbb{R}`.



But this relation is not symmetric as `3 \geq 2` but `2 \geqq 3` i.e. `(3,2) \in R` but `(2,3) \in R`.



Also this relation is transitive as `a \geq b, b \geq c \Rightarrow a \geq c` i.e. `(a, b) \in R,(b, c) \in R \Rightarrow` `(a, c) \in R, \forall a, b, c \in \mathbb{R}`.