Answered: Prove that the following proposition is…

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

Prove that the following proposition is false: 50n + 2n^2 ∈ O(n) using any of the proving methods (induction or limits or Big O property)

Expert Solution

Step 1: Approach

To prove that the proposition $50 space plus space 2 n hat 2 not an element of O left parenthesis n right parenthesis$ is false, we can use the limits method.

In Big O notation, a function $f (n)$ belongs to $O (g (n))$ if and only if there exist positive constants $C$ and $Error converting from MathML to accessible text.$ such that $0 \leq f (n) \leq C g (n)$ for all $n \geq k$ .

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