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Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
CBSE | Class 12 | Exercise 1.1 | Maths | NCERT | Relations and Functions
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.

solution:

R = {(a, b) : a ≤ b3}

a ≤ a3: which is valid, (a, a) ∉ R, So R isn’t reflexive.

a ≤ b3 however b ≤ a3 (bogus): (a, b) ∈ R yet (b, a) ∉ R, So R isn’t symmetric.

Once more, a ≤ b3 and b ≤ c3 then a ≤ c3 (bogus) : (a, b) ∈ R and (b, c) ∈ R and (a, c) ∉ R, So R is transitive.

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

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