Answered: 6. Let a @b= max {a, b} = a if b ≤ a,…

6. Let a @b= max {a, b} = a if b ≤ a, otherwise a @ b = max {a, b} = b. Give a proof by cases that for all real numbers a, b, c (a @b) @ c-a @ (b@c)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Find the first three examples of an odd number x>0 and an even number y>0 such that x − y = 7.
= For integer n ≥ 1 let P(n) be the predicate that 9" - 5n CEZ 4c for some For the induction hypothesis, consider k ≥ 1, and suppose that P(k) is true. For the inductive step, we want to show that P(k+1) is true. True or false: The following proof correctly proves P(k+ 1) true, where every step other than the one labelled IH follows by algebra. (I'm asking: is this a valid algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the correct final result?) 9k+15k+19.9k - 5.5k True False = 9(4c – 5k) – 5 ⋅ 5% for CE Z by the IH = 4.9c-9.5k - 5.5k = 4.9c-4.5k = 4d for d = Z
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
Use strong induction to prove the following:
3. Let p(n) = Σª a¡n², where a¿ > 0, be a degree-d polynomial in n, and let k be a constant. Prove the following properties. if k ≥ d, then p(n) = 0(nk); if k ≤d, then p(n) = N(nk); if k = d, then p(n) = 0(nk); if k > d, then p(n) = o(n²); if k < d, then p(n) = w(nk); a. b. C. d. e.
. Consider the alphabet Σ = {0,1}. Give regular expressions generating the following lan- guages. (a) {w ¤ Σ* | w begins with a 0 and ends with a 1} (b) {w € Σ* | w contains at least four Os} 1* (c) {w € Σ* | w contains the substring 1101} (d) {w € Σ* | w has length at least 4 and its third symbol is a 0} (e) {w € Σ* | w begins with a 0 and has even length, or begins with a 1 and has odd length} (f) {€,0} (g) The empty set (h) All strings over Σ (i) All strings over Σ except the empty string
Use Numpy to complete the following task(s). 8. Solve Assignment 5.1 #4a. 4. Let A = [2] 21 a. Give the characteristic equation of A and verify that A satisfies the characteristic equation. Characteristic equation of (A) = |xI - A| = 0
Formally prove that on? + 10n + 10 = (n²) using the definition of 2(:).
In this group of problems, you are given the predicate P(x), where the domain of x is the set of natural numbers.
Consider this function:boolean freaky(n) {// PRE: n is a positive integer// POST: ???if n < 2: return falsex = 2while x < n { if n mod x == 0 return false x = x + 1}return true}(i) Find the postcondition of this function(ii) Find the best possible big-oh bound for its complexity(iii) What can we say about big-thetacomplexity for this function?
Let A = {1, 13, 100} and B = {7, 13}. Then: (d) What is the powerset of B? (e) What is { (f) What is { € A | Vy € B, x > y} € A ³y € B,x > y}
DO NOT COPY FROM OTHER WEBSITES Correct and detailed answer will be Upvoted else downvoted directly. Thank you!