# With proper explanation.

Solution:

R = {(*a*,*b*): *a* ≤ *b*^{2}}

It can be observed that ( 1/2 , 1/2 ) does not belongs to R.

since, 1/2 > (1/2)^{2} = 1/4

∴Ris not reflexive.

Now, (1,4) ∈ R as 1 < 4^{2}

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

∴(4,1) ∉ R

∴Ris not symmetric.

Now,

(3, 2),(2, 1.5) ∈ R

(as 3 <2^{2} = 4 and 2 < (1.5)^{2} = 2.25)

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

∴(3,1.5) ∉ R

∴ Ris not transitive.

Hence, Ris neither reflexive, nor symmetric, nor transitive.

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