BIG 0 practicetrue or false and explain why true or false 5. \( n \log^2 n = O(n^2) \)6. \( n \log^2 n = 2^{O(n)} \)This transcription contains mathematical equations typical in algorithm analysis, dealing with asymptotic notation. Here, \( n \) is a variable often representing the size of the input, and \( O \) is the Big O notation used to describe an upper bound on the time complexity of an algorithm.- In equation 5, \( n \log^2 n = O(n^2) \), it suggests that the function \( n \log^2 n \) grows at a rate that is eventually slower than or equal to that of \( n^2 \).- In equation 6, \( n \log^2 n = 2^{O(n)} \), it implies that the function \( n \log^2 n \) grows at a rate slower than or equal to an exponential function \( 2^n \).

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5. n log? n = 0(n²) 6. n log n 20(n) n 3=

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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Question

BIG 0 practice

true or false and explain why true or false

5. \( n \log^2 n = O(n^2) \)

6. \( n \log^2 n = 2^{O(n)} \)

This transcription contains mathematical equations typical in algorithm analysis, dealing with asymptotic notation. Here, \( n \) is a variable often representing the size of the input, and \( O \) is the Big O notation used to describe an upper bound on the time complexity of an algorithm.

- In equation 5, \( n \log^2 n = O(n^2) \), it suggests that the function \( n \log^2 n \) grows at a rate that is eventually slower than or equal to that of \( n^2 \).

- In equation 6, \( n \log^2 n = 2^{O(n)} \), it implies that the function \( n \log^2 n \) grows at a rate slower than or equal to an exponential function \( 2^n \).

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