The Relation R = {(x, y) : x ≤ y²} defined on the set R of Real numbers is :

(A) reflexive but not symmetric

(B) neither reflexive nor symmetric

(C) neither reflexive nor transitive

(D) reflexive but not transitive

(E) not reflexive but symmetric

Choose the correct answer from the options given below : 

(A) and (C) only

$R={(x,y):x≤y^2}$

It can be observed that $(\frac{1}{2}​,\frac{1}{2}​)∉R$, since $\frac{1}{2}​>(\frac{1}{2}​)^2=\frac{1}{4}$.

∴R is not reflexive.

Now, (1,4) ∈ R as 1 < 4²

But, 4 is not less than 12.

∴ (4,1) ∉ R

∴ R is not symmetric.

Now, (3,2),(2,1.5) ∈ R

(as 3 < 2² = 4 and 2 < (1.5)² = 2.25)

But, 3 > (1.5)² = 2.25

∴ (3, 1.5) ∉ R

∴ R is not transitive.

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