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a. If t(n) = O(g(n)), then g(n) = N(t(n)). b. 9(ag(n)) = 8(g(n)), where a > 0. c. O(g(n)) = O(g(n)) ♬N(g(n)).

a. If t(n) = O(g(n)), then g(n) = N(t(n)). b. 9(ag(n)) = 8(g(n)), where a > 0. c. O(g(n)) = O(g(n)) ♬N(g(n)).

Database System Concepts
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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Please prove the following assertions by using the definitions of the notations involved, or disprove them by giving a specific counterexample.

a. If t(n) = O(g(n)), then g(n) = N(t(n)). b. (ag(n)) = (g(n)), where a > 0. c. O(g(n)) = 0(g(n)) ♬ N(g(n)).
Transcribed Image Text:a. If t(n) = O(g(n)), then g(n) = N(t(n)). b. (ag(n)) = (g(n)), where a > 0. c. O(g(n)) = 0(g(n)) ♬ N(g(n)).
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