C) Find the smallest ? so that ?(?) = 7?2(log ?)3 + 2?4 + 3(log ?)2...
Prove whether or not the program segment x≔3 z≔x-y+2 if y>0 then z≔z+3 else z≔2 is partially correct with respect to the initial assertion y=4 and the final assertion z=6
Let f(x) be the recurrence relation defined by fn=fn-12+nfn-2 for n≥2 f0=3 f1=-1 Find f(3)
Solve and show work for problem 8 Problem 8. Consider the sequence defined by ao = 1, ai-3, and a',--2an-i-an-2 for n Use the generating function for this sequence to find an explicit (closed) formula for a 2. Problem 1. Let n 2 k. Prove that there are ktS(n, k) surjective functions (n]lk Problem 2. Let n 2 3. Find and prove an explicit formula for the Stirling numbers of the second kind S(n, n-2). Problem 3. Let n 2...
For part (a), please prove the answer. 5. Let S = {1, 2, 3, 4} and let F be the sets of all functions from S to S. Let R be the relation on F defined by: For all f,g EF, fRg if and only if fog(1)-2. (a) Is R reflexive? symmetric? transitive? (b) Is it true that that there exists f E F so that fRf? Prove your answer. (c) Is it true that for all f F, there...
3. Let f(a) 990 (a) Use the differentials to estimate 990 (b) Apply Newton's method to the equation f(z) = 0, derive the recurrence relation of r, and 2,-,, (c) Use Newton's method with initial approximation 퍼 10 to find 8p the third approximation to the root of the equation f(a)0. 3. Let f(a) 990 (a) Use the differentials to estimate 990 (b) Apply Newton's method to the equation f(z) = 0, derive the recurrence relation of r, and 2,-,,...
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
Consider the following: Algorithm 1 Smallest (A,q,r) Precondition: A[ q, ... , r] is an array of integers q ≤ r and q,r ∈ N. Postcondition: Returns the smallest element of A[q, ... , r]. 1: function Smallest (A , q , r) 2: if q = r then 3: return A[q] 4: else 5: mid <--- [q+r/2] 6: return min (Smallest(A, q, mid), Smallest (A, mid + 1, r)) 7: end if 8: end function (a) Write a recurrence...
4. Let 3 be the relation on Z2 defined by (a,b) 3 (c,d) if and only if a Sc and b < d. (a) Prove that is a partial order. (b) Find the greatest lower bound of {(1,5), (3,3)}. (c) Is < a total order? Justify your answer.
please solve only part(a) and part(b) Problem 7. A 2 × n clockerboard is to be tiled using three types of tiles. The first tile is a white 1 x 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 x 2 tile. Let t(n) denote the number of tilings of the 2 × n checkerboard using white red and black tiles. (a) Find a recursive formula for t(n)...
Discrete mathematics 2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2 5: 01, 0, 12, 2 because the strings 00,02, 20, 22 are not allowed, as they have adjacent even digits. As another example, the string 10112 is allowed, while the strings 10012 and 120121 are not allowed (a) Find #3; (b) find...