Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS...

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE.

Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS TRUE

Expert Solution

Here we will use the basic definitions of omega asymptotic function, small-o asymptotic function and theta asymptotic function while solving these problems.

1) First of all, we will consider f(n)=big omega(g(n)) :

We have proved that f(n)=big omega(g(n)) then f(n)=o(g(n)) is never true.

2) We have to note that the result of max(f(n),g(n)) is either f(n) or g(n) [ i.e. whichever is maximum will be the result]

The sum of f(n) and g(n) is always greater than or equal to individual f(n) and individual g(n).

We have proved that f(n) +g(n) =Theta(max(f(n),g(n)) is always true.

venereology answered 1 year ago

If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))

1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that...

1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that 5n2 – 15n + 100 is Θ(n2 ) 3.)Is 5n2 O(n)?

1. Find the big−O, big−Ω estimate for x7y3+x5y5+x3y7. [Hint: Big-O, big- Θ, and big-Omega notation can...

1. Find the big−O, big−Ω estimate for x7y3+x5y5+x3y7. [Hint: Big-O, big- Θ, and big-Omega notation can be extended to functions in more than one variable. For example, the statement f(x, y) is O(g(x, y)) means that there exist constants C, k1, and k2 such that|f(x, y)|≤C|g(x, y)|whenever x > k1 and y > k2] 2. Find a div b and a mod b when: (a) a = 30303, b = 333 (b) a = −765432, b = 3827 3. Convert...

(a) Explain the difference between big-O and big-theta, and give examples of each to show the...

(a) Explain the difference between big-O and big-theta, and give examples of each to show the difference. (b) How can we say that two functions have the same asymptotic complexity, using big-theta notation? (c) Rank the following functions in order of increasing complexity (rate of growth), and indicate which functions have the same asymptotic complexity. x2; x log(x); 2x; log(x) + 7; 92x2 + 57x + 3921; 4x; 27x2 + 8x3; 22x+5; log(x42); 3x + 12.

Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where...

Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where f(n) and g(n) are positive functions. ω(n) + ω(n2) = theta(n). f(n)g(n) = ω(f(n)), where f(n) and g(n) are positive functions. If f(n) = theta(g(n)), then f(n) = theta(20 g(n)), where f(n) and g(n) are positive functions. If there are only finite number of points for which f(n) > g(n), then f(n) = O(g(n)), where f(n) and g(n) are positive functions.

if a in G (group ) such as o(a)=mn prove the existence of g and h...

if a in G (group ) such as o(a)=mn prove the existence of g and h in G such as a=gh=hg and o(g)=m o(h)=n

Prove that 1+ cos theta + cos 2theta + .... cos ntheta = 1/2 + (sin(n+1/2)theta)/2sin(theta/2)

Prove and give a counterexample: If N ⊲ G and G ⊲ H, then N ⊲...

Prove and give a counterexample: If N ⊲ G and G ⊲ H, then N ⊲ H. Please write an explanation with some details

State whether each of the following is always true (T) or not always true (F). a)...

State whether each of the following is always true (T) or not always true (F). a) If X is a random variable, Corr X, (1/3)X= (1/3). b) If X and Y are independent random variables then E(X|Y ) = E(X) c) d) If fx(x) is the marginal density of a random variable X and fy(y|X = x) is the conditional density of a random variable Y , given a particular realization x of X, then the joint density of X...

For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is...

For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is 1-to-1 b) Prove: f is onto c) Prove {1, 2} x N is countable

Question