Q1E Question: Answer each part TRUE ... [FREE SOLUTION]

91影视

Introduction to Theory of Computation

Michael Sipser

Computer Science

3rd Edition 路 458 pages

ISBN: 9781133187790

Chapter 0: Q1E (page 1)

Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) 路 A c . n^{2} = O (n l o g 2 n) 路 A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$

Short Answer

Expert verified

(a) $2 n = O (n)$ is True.

(b) $n^{2} = O (n)$ isFalse.

(d) $n \log n = O (n^{2})$ isTrue.

(e) $3 n = O (2 n)$ isFalse.

(f) $2^{2 n} = O (2^{2 n})$ is True.

Step by step solution

To check whether 2n = O(n) True or false

a) $2 n = O (n)$ isTrue

Suppose. $c = 2 鈥� 2 n 猢� c n = 2 n 鈥� f o r 鈥� a l l 鈥� n > = 1$

Thus Big-O holds.

To check whether O(n)n2=O(n) True or false

b) $n^{2} = O (n)$ isFalse

$n^{2} = c n 鈥� n^{2} < = c n 鈥� f o r 鈥� a l l 鈥� n > = n_{0}$ doesn鈥檛 hold.

To check whether n2=O(nlog2n) True or false

c) $n^{2} = O (n \log^{2} n)$ isFalse

There doesn鈥檛 exist positive constants $n_{0}$ and c such that $n^{2} 猢� c n 鈥� \log^{2} n 鈥� f o r 鈥� a l l 鈥� n > = n_{0}$ .

To Find whether nlogn=O(n2) True or false

d) $n \log n = O (n^{2})$ isTrue

$l o g 鈥� n = O (n)$ there exist positive constants c and n0 such that log $n 猢� c n 鈥� f o r 鈥� a l l 鈥� n > = n_{0}$ .

To Find whether n = 2O(n) True or false

e) $3 n = 2 O (n)$ isFalse

there doesn鈥檛 exist constants c and n0 such that $3 n 猢� c^{2} n 鈥� f o r 鈥� a l l 鈥� n > = n_{0}$ .

To Find whether 22n=O(22n) True or false

f) $2^{2 n} = O (2^{2 n})$ isTrue

We know any function $f (n) 鈥� i s 鈥� O (f (n))$ .

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91影视

Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) 路 A c . n^{2} = O (n l o g 2 n) 路 A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$

Short Answer

Step by step solution

To check whether 2n = O(n) True or false

To check whether O(n)n2=O(n) True or false

To check whether n2=O(nlog2n) True or false

To Find whether nlogn=O(n2) True or false

To Find whether n = 2O(n) True or false

To Find whether 22n=O(22n) True or false

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91影视

Question: Answer each part TRUE or FALSE.a.2n=O(n)b.n2=O(n)路Ac.n2=O(nlog2n)路Ad.nlogn=O(n2)e.3n=2O(n)f.22n=O(22n)

Short Answer

Step by step solution

To check whether 2n = O(n) True or false

To check whether O(n)n2=O(n) True or false

To check whether n2=O(nlog2n) True or false

To Find whether nlogn=O(n2) True or false

To Find whether n = 2O(n) True or false

To Find whether 22n=O(22n) True or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Blockchain Technology

Computer Programming

Computer Network

Algorithms in Computer Science

Theory of Computation

Problem Solving Techniques

Study anywhere. Anytime. Across all devices.

Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) 路 A c . n^{2} = O (n l o g 2 n) 路 A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$