Let f(n) = 2n – n² + 10n – 7. Show that f(n) is O(n³) using specific values of C and no-
Q: Let g(n) = 13 + g(n) = 0(n4) giving the constants. + 23 + + n3. Show that %3D
A: According to principle methemetical induction 13 + 23 + 33 + … + n3 = (n(n+1)2)2 On Solving this we…
Q: Give the cardinality of the power set of set B = {{a, b, c}}. %3D 3 O 8 O 2 O 4
A: The cardinality of a set is the number of distinct elements in the set. A power set includes all the…
Q: Prove the following equality: (n+3)(n+2) 2 n+3 n+1 for n-1
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Q: Consider the following code fragment. Compute the worst-case time complexity in terms of n. for…
A: Kindly note, there are two separate questions posted. As per our guidelines, we are allowed to one…
Q: for the given 1,2,3 find the recurrences - the closed-form expression for n. 1) S(0) = 6 for n =…
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Q: with n=6 and A=(3,5,4,1,3,2). Draw the corresponding walkthrough as shown
A: The answer given as below:
Q: Demonstrate that n! equals O (nn).
A: According to the information given:- We have to prove n!=O(nn)
Q: Given a list of n positive integers, show that there must two of these integers whose difference is…
A: - We need to show that there must be two integers in a n length list whose difference is divisible…
Q: 5. Define the following (almost Fibonacci) recurrence for n = 0 Gn for n = 1 Gn-1+Gn-2+1 for n2 2…
A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…
Q: Let, a1 = 3, a2 = 4 and for n ≥ 3, an = 2an−1 + an−2 + n2 , express an in terms of n.
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Q: log 2 (x +3) x2 +3x + 2 Find the domain of definition of f (x)=
A: Solution :-_
Q: 1. If n is any natural with n 2 3, there are at least two numbers in the set {0,.., n-1} whose…
A: It is necessary to find multiplicative inverse modulo n in the set. if n is any natural with n>=3…
Q: 1. Let x ∈ Z. Use a direct proof to show that if 5x2 + 8 is odd then x is odd. 2. Show by…
A: 1) Given 5x2+8 is odd which implies 5x2 is odd as the sum of any odd and even is odd. so 5x2 is…
Q: find c and n0 to prove 16n@ E )(n^2)
A: Suppose that when n=kn=k (k≥4)(k≥4), we have that k!>2kk!>2k. Now, we have to prove that…
Q: 3. Prove that (P = Q) = R has the same truth with (P = R) ^ (Q = R). We write (P=Q)=R= (P=R) ^ (Q =…
A: We need to prove the given statement.
Q: Show that n^3+5n is not O(n^2).
A: Here we have to show n^3+5n is not O(n^2)
Q: For the two chains of number sets given here, derive a rule for moving along an arrow, and a rule…
A: Given two chains are, {57,36}→{21,36}→{21,15}→{6,15}→{6,9}→{6,3}→{3,3}={3} stop…
Q: Given f(n) ∈ Θ(n), prove that f(n) ∈ O(n²). Given f(n) ∈ O(n) and g(n) ∈ O(n²), prove that…
A: Asymptotic notations (Θ, O, Ω) compares a time complexity function with another standard function…
Q: В4 Order the following functions by asymptotic growth rate. 4nlogn + 2n, n log (n²), 2º, 4n, 2*, n²…
A: 1 < logn < n < n < nlogn < n2 < n3 < ...... <nn Lower Bound…
Q: c) Prove or disprove that if n2- -n is even then n is even
A: n2-n can also be written as: n(n-1)
Q: Find f(1), ƒ (2), ƒ (3), and f (4) if ƒ (n) is defined recur- sively by f(0) = 1 and for n = 0, 1,…
A: As per our guidelines, only one question or three sub parts will be answered. So, please repost the…
Q: Given f(n) E O(n), prove that f(n) E O(n²). Given f(n) E O(n) and g(n) E O(n²), prove that f(n) g(n)…
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Q: et p> 2 be a prime, g a generator of Z*p. Provide an efficient algorithm which, given x e *p,…
A:
Q: f(n) ∈ Θ(n), prove that f(n) ∈ O(n²).
A: Given f(n) ∈ Θ(n), prove that f(n) ∈ O(n²
Q: 2. Show that if n is less than 31, then xn can be shown to be in POLYNOMIAL in fewer than eight…
A: 3 rules of POLYNOMIAL RULE 1: Any number is in POLYNOMIAL RULE 2: The variable x is in POLYNOMIAL…
Q: Question 2. (a) Show that there is no n EN such that n = 1 (mod 12) and n = 3 (mod 8). (b) Find a…
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Q: (1) (a) Show that n(n2 - 1)(n + 2) is divisible by 4 for all integer n.
A: For any integer n, either (n−1) or n must be even; and, therefore their product is also even. So we…
Q: 3. Let the "Tribonacci sequence" be defined by T₁ = T₂ = T₁=1 and T₁ = T₁+T2+T-3 for n ≥4. Prove…
A: A Tribonacci sequence or series is a sequence of integers such that each term from the fourth onward…
Q: Find and show the complexity of these questions : 1- T(n)= T(n-1)+ T(n-2) + c T(0) = 1 T(1)= 1
A: The time complexity of the algorithms is the perfect measure of the efficiency of program. The time…
Q: Q/ Given a sequence x(n), n from 0 to 3, where x(0)=-2, x(1)=4, x(2)=0 and х(3)--5 Evalute its DFT…
A: There are two ways to answer the above questions 1. Find the inverse fourier transform then…
Q: 4. Consider f(n) = 3n2 + 4n – 3, mathematically show that f(n) is O(n?), 2(n²), and O(n2).
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Q: Show that n2 + 3n + 2 is O(n²). Show that 3" is N(n° + 4).
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Q: Show that n! = 0(n").
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Q: Prove that if x∈R and x >−1, then(1 +x)n≥1 +nx for all n∈N
A: since 10>4+1 I will use this theory Let P(n):(1+x)^n>=(1+nx), for x>-1 Let n=1,…
Q: x <-- 1 for i = 1 to n do x <-- 2 x for j = i to sqrt{n} do for k = 1 to n^3 do x <-- x +1 k<-- 2 k
A: Answer to the above question is in step2.
Q: Show that 5n+5 is O(n). (pick c and n0)
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Q: Arrange the functions √n (square root of n), 1000log(n), nlog(n), 2n!, 2n, 3n, n2/100000 in…
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Q: Prove the following, or give a counter example: (a) f(n) — О(g(n)) and g(n) — - О(h(m)). O(h(n))…
A: Big –O Notation: Big O notation is the method to describe the rate of growth of a function. This…
Q: Find the closed form for each T(n) given as a recurrence: 1. 2 : n=1 T(n) = { T(n – 1) + 2 : n22 2.…
A: Note: Answering the question 4 and 5 as asked in the question. Given : T(m) = 0 , m=1 T(m) =…
Q: Show that log(n!) = O(n log(n))
A: We need to prove that, O(log(n))=O(n*log(n)).
Q: Let ENFA = {N | N is an NFA and L(N) = Ø}. ENFA is in P.
A: Let ENFA = {N | N is an NFA and L(N) = Ø}. Prove that ENFA is in P.
Q: Show that (p ∧ q) → r and (p → r) ∧ (q → r) is logically equivalent.
A: TRUTH TABLE of (p ∧ q) → r p q r p ∧ q (p ∧ q) → r) F F F F T F F T F T F T F F T F…
Q: Q. 5:1 show that: Let n and k be positive integers with n >= k. Use an algebraic proof to n+ 1 C(n +…
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Q: Prove that (n + a)^b = Θ( n^b), b > 0
A: Proof: The proof of the statement is explained in the below steps: n + ab ≤ n + ab, where n > 0≤…
Q: Give the cardinality of the power set of set B = {a,{b, c}}. O 2 O 3 O 8 O 4
A: Given set is B={a, {a, b}} Set B contains 2 elements. Number of elements in the power set= 2n where…
Q: Let n be an integer, use the definition of even to prove that 18n + 2 is even. 18n+2= Since X is an…
A: A number is said to be even if that number is a multiple of 2 and A number is said to be odd if a…
Q: (a) for any integers n a and m : if both n and m are odd, thenn – m² is even
A: a) Given, For any integers n and m : if both n and m are odd, then n - m 2 is even. The proof…
Q: The complete decimation-in-frequency algorithm is depicted for N = 16;…
A: The demonstration of 16 length sequence is given in the next step.
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- Let, a1 = 3, a2 = 4 and for n ≥ 3, an = 2an−1 + an−2 + n2, express an in terms of n.What are the complexities of the following code segments in terms of n? Give an upper bound. a) int i=1;while (i<= n) { int j = i; while (j > 0) j = j/2;i++; } b) int i,j s=0; for (i=0; i<n; i++) { i--; s++; if (s == n) { i++; s = 0; } } c) while (n > 0) { for (int i=0; i<n; i++) sum++; n = n/2; }Given f(n) ∈ Θ(n), prove that f(n) ∈ O(n²). Given f(n) ∈ O(n) and g(n) ∈ O(n²), prove that f(n)g(n) ∈ O(n³).
- Given a list of n positive integers, show that there must two of these integers whose difference is divisible by n-1Show that log(n!) = O(n log(n))Explain, with an example why the following definition, would not be suitable or useful: f(n) is Ω( g(n) ) if and only if there exists n0, such that:forall n ≥ n0, there exists c > 0 such that,f(n) ≥ c g(n)
- Give an example of a function f(n) such that f(n) ∈ O(n √ n) and f(n) ∈ Ω(n log n)) but f(n) ∈/ Θ(n √ n) and f(n) ∈/ Θ(n log n)). 2. Prove that if f(n) ∈ O(g(n)) and f(n) ∈ O(h(n)), then f(n) ^2 ∈ O(g(n) × h(n)). 3. By using the definition of Θ prove that 4√ 7n^3 − 6n^2 + 5n − 3 ∈ Θ(n 1.5 )Prove that if x∈R and x >−1, then(1 +x)n≥1 +nx for all n∈NIt was claimed that:(a, b) ≤ (c, d) ⇔ (a < c) ∨ (a = c ∧ b ≤ d) defines a well-ordering on N x N. Show that this is actually the case.
- Let the sequence (n) be recursively defined by x1 = √2 and Xn+1 = √√2+xn, n≥ 1. Show that (n) converges and evaluate its limit.Suppose we want to show that 100n + 5 is in the set O(n). If we let n0 = 5, then the smallest choice for c is ___.Show Let f(.) be a computable, strictly monotonic function, that is, f(n+ 1) > f(n) for all n. Show B = {f(n) | n ∈ N} is recursive.