State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

Question

Philoid · Accepted Answer

Let A be any set A relation R on A is said to be a transitive relation if

(a,b) Є R & (b,c) Є R

(a,c) Є R for all a,b,c Є A

A = {1,2,3} and R = {(1,2),(2,1)}

As per the definition of transitive element,

If (1,2) Є R and (2,1) Є R then (a,c) Є R or (1,1) Є R but it is missing in the R.

it is not a transitive relation.