Prove or Disprove (4 Marks)a. ¼ n 2 - 2n + ½ Ɛ O(n 2 )b. 4n 2 + 25 n – 2010 =  (n2)c. 8n 2 + 2n - 3  O(n 2 )d. 2n 2 = 4n + O(22n)

Question

Prove or Disprove (4 Marks)a. ¼ n 2 - 2n + ½ Ɛ O(n 2 )b. 4n 2 + 25 n – 2010 =  (n2)c. 8n 2 + 2n - 3  O(n 2 )d. 2n 2 = 4n + O(22n)
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Solution 1

a. ¼ n^2 - 2n + ½ ∈ O(n^2)

To prove this, we need to show that there exist constants c and n0 such that 0 ≤ ¼ n^2 - 2n + ½ ≤ c*n^2 for all n ≥ n0.

Let's choose c = 1 and n0 = 1. Then for all n ≥ 1, we have:

0 ≤ ¼ n^2 - 2n + ½ ≤ n^2

So, ¼ n^2 - 2n + ½ ∈ O(n^2) is true.

b. 4n^2 + 25n – 2010 = Ω( Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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