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Give an example of a relation. Which is Transitive but neither reflexive nor symmetric.

Q.10 Give an example of a relation.

(ii) Which is transitive but neither reflexive nor symmetric.

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Let  

R = \left \{ \left ( x,y \right ): x> y \right \}

Now for x\in R ,(x,x)\notin R so it is not reflexive.

Let (x,y) \in R  i.e. x> y

Then y> x is not possible i.e. (y,x) \notin R . So it is not symmetric.

Let (x,y) \in R  i.e. x> y    and  (y,z) \in R i.e.y> z

we can write this as x> y> z

Hence,x> z  i.e. (x,z)\in R. So it is transitive.

Hence, it is transitive but neither reflexive nor symmetric.

 

 

 

 

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