Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b2} is neither reflexive nor symmetric nor transitive.

Question 2: Show that the relation R in the set R of real numbers, defined as

R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive.

Answer: R = {(a, b): a ≤ b²}

It can be observed that 

∴R is not reflexive.

Now, (1, 2) ∈ R as 1 < 2²

But, 2 is not less than 1².

∴ (2, 1) ∉ R

∴R is not symmetric.

Now,

(5, 3), (3, 2) ∈ R

(as 5 < 3² = 9 and 3 < (2) ² = 4)

But, 5 > (2) ²= 4

∴ (5, 2) ∉ R

∴ R is not transitive.

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