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Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false 1. If f(n) = Θ(n), then nf(n) = Θ(n2 ) 2. If f(n) = O(n2 ) and g(n) = Ω(f(n)), then g(n) = O(n2) 3. If f(n) = O(0. 5n2 ) and f(n) = Ω(7n2 + nlogn), then f(n) = Θ(n2 )

Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false 1. If f(n) = Θ(n), then nf(n) = Θ(n2 ) 2. If f(n) = O(n2 ) and g(n) = Ω(f(n)), then g(n) = O(n2) 3. If f(n) = O(0. 5n2 ) and f(n) = Ω(7n2 + nlogn), then f(n) = Θ(n2 )

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
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Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false

1. If f(n) = Θ(n), then nf(n) = Θ(n2 )

2. If f(n) = O(n2 ) and g(n) = Ω(f(n)), then g(n) = O(n2)

3. If f(n) = O(0. 5n2 ) and f(n) = Ω(7n2 + nlogn), then f(n) = Θ(n2 )

4. If f(n) = O(n3 ), then f(n) = Ω(2n3 )

5. If f(n) = Θ(n3 ), then f(n) = O(2n )

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