Assertion (A): If , then mathematically . Reason (R): Big-O and Big-Omega asymptotic notations are symmetric duals of each other.

Both (A) and (R) are true, and (R) is the correct explanation of (A) Explanation: Analysis of Assertion (A): By definition of Big-O: means there exist positive constants and such that: Dividing by , we get: By definition of Big-Omega ( ), this implies with constant . Therefore, Assertion (A) is True. Analysis of Reason (R): The property is known as transpose symmetry (or symmetric duality) between upper bound ( ) and lower bound ( ). Therefore, Reason (R) is True. Relationship between (A) and (R): The symmetric dual relationship between and is precisely the mathematical reason why implies . Hence, (R) is the correct explanation of (A).

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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

Assertion (A): If $f (n) = O (g (n))$ , then mathematically $g (n) = Ω (f (n))$ .

Reason (R): Big-O and Big-Omega asymptotic notations are symmetric duals of each other.

Choose the correct answer: