HomeworkLib
Question

Let f(n) and g(n) be non-negative functions such that f(n) is O(g(n)) and g(n) is O(f(n))....

Let f(n) and g(n) be non-negative functions such that f(n) is O(g(n)) and g(n) is O(f(n)). Use the definition of “big Oh” to prove that f(n)−g(n) is O(f(n)).

engineering   Computer-Science   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

******************************************************************************************
Please Upvote the answer as it matters to me a lot :)
*****************************************************************************************
As per HomeworkLib expert answering guidelines,Experts are supposed to answer only certain number of questions/sub-parts in a post.Please raise the remaining as a new question as per HomeworkLib guidelines.
******************************************************************************************


0 0
Add a comment
Know the answer?
Add Answer to:
Let f(n) and g(n) be non-negative functions such that f(n) is O(g(n)) and g(n) is O(f(n))....
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove...

    1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...

  • Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)),...

    Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f(n) = O (h (n)). You may assume that low degree (i.e., low-exponent) polynomials do not dominate higher degree polynomials, while higher degree polynomials dominate lower ones. For example, n^3 notequalto O (n^2), but n^2 = O (n^3). Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily...

  • (5) Let (. A, /u) be a measure space. Let f,g : O > R* be a pair functions. Assume that f is measurable and that f =...

    (5) Let (. A, /u) be a measure space. Let f,g : O > R* be a pair functions. Assume that f is measurable and that f = g almost everywhere. (a) Prove that q is measurable on A. Prove that g is integrable (b) Let A E A and assume that f is integrable on A and A (5) Let (. A, /u) be a measure space. Let f,g : O > R* be a pair functions. Assume that...

  • For each pair of functions f(n) and g(n), indicate whether f(n) = O(g(n)), f(n) = Ω(g(n)), and/or...

    For each pair of functions f(n) and g(n), indicate whether f(n) = O(g(n)), f(n) = Ω(g(n)), and/or f(n) = Θ(g(n)), and provide a brief explanation of your reasoning. (Your explanation can be the same for all three; for example, “the two functions differ by only a multiplicative constant” could justify why f(n) = n, g(n) = 2n are related by big-O, big-Omega, and big-Theta.) i. f(n) = n^2 log n, g(n) = 100n^2 ii. f(n) = 100, g(n) = log(log(log...

  • Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures....

    Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures. f(n) = O(g(n)) implies g(n) = Ω(f(n)) . f(n) = O(g(n)) implies g(n) = O(f(n)). f(n) + g(n) = Θ(min(f(n),g(n))).

  • Q4 Let F denote a countably infinite set of functions such that each f; e F...

    Q4 Let F denote a countably infinite set of functions such that each f; e F is a function from Z+ to R+, and let R be a homogeneous binary relation on F where R = {(fa, fb) | fa(n) € (fo(n))}. Prove that R is a reflexive relation. In your proof, you may not use a Big-12, Big-0, or Big- property to directly justify a relational property with the same name; instead, utilize the definition of Big-12, Big-O, and...

  • Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n)...

    Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...

  • Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of _-notation, prove...

    Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of _-notation, prove that max( f (n), g(n)) = Θ( f (n) + g(n)).

  • Let n be a non-negative integer. Letf() be such that f(x), f'(x).f"(x).,fn+exist, and are continu...

    Let n be a non-negative integer. Letf() be such that f(x), f'(x).f"(x).,fn+exist, and are continuous, on an interval containing a. In this assignment, you will prove by induction on n that for any r in that interval f'(c) f"(c) fm (c) (t) (x -t)" dt. 7n n! 1. (a) Explain why the claim given above is true for n-0 (b) Use the fact that the claim is true for n-0 to explain why the claim is true for n =...

  • I. Functions and Isomorphisms. Let G be a group and let a EG be any non-identity...

    I. Functions and Isomorphisms. Let G be a group and let a EG be any non-identity element (so a #e). Define a function f : GG so that, for any r EG, f(x) = (xa)-1 (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer. (c) Is f an isomorphism? Prove your answer.

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT