Q. 10D4.0( 27 Votes )

# Give an example o

Answer :

| Let us define a relation R in R as

R = {(a,b) : a^{3} ≥ b^{3}}

It is clear that (a,a) ϵ R as a^{3} = a^{3}

⇒ R is reflexive.

Now, (2,1) ϵ R

But (1,2) ∉ R

⇒ R is not symmetric.

Now, let (a,b) (b,c) ϵ R

⇒ a^{3}≥ b^{3} and b^{3}≥ c^{3}

⇒ a^{3}≥ c^{3}

⇒ (a,c) ϵ R

⇒ R is transitive.

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

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