Answer :

It is given that R = {(a, b) : a ≤ b2}

Check for reflexive:

We can see that


Since,


Therefore, R is not reflexive.

Check for symmetric:

Now, (1,4) ϵ R as 1 < 42


But 4 is not less than 12.


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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