Each of the following assertions is either True or False. Write your answer legibly beside each question. Do not justify your answer. (e) n = 0(n2) and n2 = 0(n)(f) cos(n) = 0(1).(g) A tree with n vertices has n - 1 edges.(h) If p is a prime number and gcd(a, p) = 1 then aP-1) = 1 (mod p).

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Description: Each of the following assertions is either True or False. Write your answer legibly beside each question. Do not justify your answer. (e) n = 0(n2) and n2 = 0(n)(f) cos(n) = 0(1).(g) A tree with n vertices has n - 1 edges.(h) If p is a prime number a

Answered: (e) n = 0(n²) and n2 = 0(n) (f) cos(n)…

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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Each of the following assertions is either True or False. Write your answer legibly beside each question. Do not justify your answer.

(e) n = 0(n2) and n2 = 0(n)
(f) cos(n) = 0(1).
(g) A tree with n vertices has n - 1 edges.
(h) If p is a prime number and gcd(a, p) = 1 then aP-1) = 1 (mod p).

Expert Solution

Step 1

solution

$(e) n = O (n^{2}) and n^{2} = O (n)$

False

as because

$n = O (n) and n^{2} = O (n^{2})$

$(f) \cos (n) = O (1)$

True

as because

we can get the result directly from the recurrence relation of cosine function

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