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Home » 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.
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.
CBSE | Class 12 | Exercise 1.1 | Maths | NCERT | Relations and Functions
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.

Solution:

R = {(a, b) : a ≤ b2} , Relation R is characterized as the arrangement of genuine numbers. (a, a) ∈ R then a ≤ a2 , which is bogus. R isn’t reflexive.

(a, b)=(b, a) ∈ R then a ≤ b2 and b ≤ a2, it is bogus articulation. R isn’t symmetric. Presently, a ≤ b2 and b ≤ c2,then a ≤ c2 , which is bogus. R isn’t transitive

In this way, R is neither reflexive, nor symmetric and nor transitive.

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