R = {(a, b) : a ≤ b3}(i) Since (a, a) ∉ R as a ≤ a3 is not always true[Take a = 1/3. then a ≤ a3 is not true]∴ R is not reflexive.(ii) Also (a, b) ∈ R ⇏ (b, a) ∈ R[Take a = 1, b = 4, ∴ 1 ≤ 43 but 4 ≰ (l)3 ]∴ R is not symmetric.(iii) Now (a, b) ∈ R, (b, c) ∈ R ⇏ (a, c) ∴ R[Take a = 100, b = 5, c = 3, ∴ 100 ≤ 53, 5 ≤ 33 but 100 ≥ 33] R is not symmetric.
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