Let `A={0,\ 1,\ 2,\ 3}` and `R` be a relation on `A` defined as `R={(0,\ 0),\ (0,\ 1),\ (0,\ 3),\ (1,\ 0),\ (1,\ 1),\ (2,\ 2),\ (3,\ 0),\ (3,\ 3)}` , is `R` reflexive? symmetric transitive?

Answer

R is reflexive , symmetric but not transitive.

Explanation

R is reflexive

as,` forall a in A`, `EE(a,a) in R`.

R is symmetric

as,` forall (a,b) in R`,`EE(b,a) in R`

but not transitive

since for `(1,0) in R`

and `(0,3) in R` but `(1,3) notin R`.