Q. 10D3.9( 21 Votes )

# Give an example of a relation. Which is

Reflexive and transitive but not symmetric.

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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Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

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