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Tell whether each of the following statements is true or false. No explanation is needed. i n? +3 = 0(n²) ii 19n = 0(n) iii log2 n = 0(log3 n)

Tell whether each of the following statements is true or false. No explanation is needed. i n? +3 = 0(n²) ii 19n = 0(n) iii log2 n = 0(log3 n)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Discrete math help please
Tell whether each of the following statements is true or false. No explanation is needed. i. \( n^2 + 3 = O(n^2) \) ii. \( 19n = O(n) \) iii. \( \log_2 n = O(\log_3 n) \) iv. \( 34n^3 + 2 = \Theta\left(\frac{n}{1000}\right) \) v. \( 123 = O(n!) \) vi. \( n^2 = \Omega(n^2 + 4) \) vii. \( n^2 = \Omega(123) \) viii. \( 3 \log_2 n = \Theta(n \log_3 n) \) ix. If \( f(n) = \Theta(g(n)) \) then \( f(n) = O(g(n)) \) x. If \( f(n) = \Omega(g(n)) \) then \( f(n) = O(g(n)) \) xi. If \( f(n) = O(g(n)) \) then \( g(n) = O(f(n)) \)
Transcribed Image Text:Tell whether each of the following statements is true or false. No explanation is needed. i. \( n^2 + 3 = O(n^2) \) ii. \( 19n = O(n) \) iii. \( \log_2 n = O(\log_3 n) \) iv. \( 34n^3 + 2 = \Theta\left(\frac{n}{1000}\right) \) v. \( 123 = O(n!) \) vi. \( n^2 = \Omega(n^2 + 4) \) vii. \( n^2 = \Omega(123) \) viii. \( 3 \log_2 n = \Theta(n \log_3 n) \) ix. If \( f(n) = \Theta(g(n)) \) then \( f(n) = O(g(n)) \) x. If \( f(n) = \Omega(g(n)) \) then \( f(n) = O(g(n)) \) xi. If \( f(n) = O(g(n)) \) then \( g(n) = O(f(n)) \)
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