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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...
"2. We say that a group G is cyclic if there exists an element g ∈ G such that G = (g) := {gn | n ∈ Z} Given any group homomorphism φ : G H, say if each of the following is true or false, and justify. (i) If φ is surjective and G is cyclic, then H is cyclic. (ii) If φ is injective and G is cyclic, then H is cyclic. (iii) If φ is surjective and...
Anyone can help? Thanks! Question 1. [5 pts) In the following problems, a, b and c are positive constants, In n stands for the natural logarithm of n. a) True or false: If f(n) = an + bnº.5, then f(n) = O(n). b) True or false: If f(n) = ans + bn + c, then f(n) = 0 (n?). c) True or false: If f(n) = an', then f(n) = N(Inn). d) Let f(n) = $1=1 give a Big- notation...
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...
11. Let an >0 and assume that bn = n+1 + B. What can we say about the convergence of an? an
please check answers thank you! Let f(n) = nt.1, g(n) = n(log2 n) Q2.1 1 Point f= O(g) O true O false Q2.2 1 Point g= O(f) O true false Q2.3 1 Point f = o(9) true false Q2.4 1 Point g= o(f) true O false Q2.5 1 Point f = (g) O true false
11. When we say that a measurement instrument such as the SAT is a standardized test, we mean that the scores on it tend to form a standard normal distribution. True False QUESTION 12 12. What measure of variability is the square root of the variance? the mean a. Ob. the mean deviation O c the standard deviation Od. the inter-quartile range QUESTION 13 13. What measure of variability uses only two case values in its computation? the range al...
QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find Cand k such that f(x) < Cg(x) for all x > k. QUESTION 4 Finding the smallest number in a list of n elements would use an OU) algorithm.
1 question) Arrange the following in the order of their growth rates, from least to greatest: (5 pts) n3 n2 nn lg n n! n lg n 2n n 2 question)Show that 3n3 + n2 is big-Oh of n3. You can use either the definition of big-Oh (formal) or the limit approach. Show your work! (5 pts.) 3 question)Show that 6n2 + 20n is big-Oh of n3, but not big-Omega of n3. You can use either the definition of big-Omega...
For f(n) = 1000 · 2" and g(n) = 3" we have: g(n) = O(f(n)) O g(n) =(f(n)) O g(n) = 2(f(n))