4. More asymptotic notation. For the following questions use the definitions of O, N, and e, not our various results about them. Prove or disprove that: if f: N→ R20, ke R+, and f(n) = O(n), then log₂ (f(n)) = O(log₂n). Prove that: if f1, f2: N→ R20, f₁ € O(91), and f2 € O(92), then f1 + f2 € O(max(91, 92)). Here, (f1 + f2)(n) = f(n) + f2(n) and max(91, 92) (n) = max(91 (n), 92 (n)).

4. More asymptotic notation. For the following questions use the definitions of O, N, and e, not our various results about them. Prove or disprove that: if f: N→ R20, ke R+, and f(n) = O(n), then log₂ (f(n)) = O(log₂n). Prove that: if f1, f2: N→ R20, f₁ € O(91), and f2 € O(92), then f1 + f2 € O(max(91, 92)). Here, (f1 + f2)(n) = f(n) + f2(n) and max(91, 92) (n) = max(91 (n), 92 (n)).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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