Q. 24.1( 183 Votes )

# Show that the rel

Answer :

It is given that R = {(a, b) : a ≤ b^{2}}**Check for reflexive:**

We can see that

Since,

Therefore, R is not reflexive.

**Check for symmetric:**

Now, (1,4) ϵ R as 1 < 4^{2}

But 4 is not less than 1^{2}.

Then, (4,1) ∉ R

Therefore, R is not symmetric.

**Check for transitive:**

Now, (3, 2), (2, 1.5) ϵ R

But, 3 > (1.5)^{2} = 2.25.

Then, (3, 1.5) ∉ R

Therefore, R is not transitive.

Therefore, R is neither reflexive, nor symmetric, nor transitive.

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