Q. 10B3.9( 24 Votes )

Give an example of a relation. Which is

Transitive but neither reflexive nor symmetric.

Answer :

Let a relation R in R defined as:

R = {(a,b): a<b}


For any a ϵ R, we have (a,a)) R as a cannot be strictly less than a itself.


In fact, a = a,


Therefore, R is not reflexive.


Now, (1,2) ϵ R but 2 > 1


(2,1)) R.


R is not symmetric.


Now, let (a,b), (b,c) ϵ R


a < b and b < c


a < c


(a,c) ϵ R


R is transitive.


Therefore, relation R is transitive but not reflexive and a symmetric.


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