Q5 of 29 Page 1

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

R = {(a, b): a ≤ b2}


It can be observed that



So, R is not reflexive.


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


So, (3, 1.5) ∉ R


Thus, R is not transitive.


Hence, R is neither reflexive nor transitive.


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