Show that the relation `R` on `R` defined as `R={(a ,\ b): alt=b}` , is reflexive and transitive but not symmetric.

Explanation

`(a,a):a≤a `is true `\AA a\in R`

hence reflexive

`(a,b)\Rightarrow a≤b,b`

`(b,a)\in R`

hence R is not symmetric

i.e.` (1,3) \Rightarrow 1≤3 but (3,1)3≤1`

`(a,b) \Rightarrow a≤b,(b,c) \Rightarrow b≤c\Rightarrow a≤c=(a,c)∈R`

hence R is transitive.