Let N be the set of all ounting numbers: 1, 2, 3,.... Consider these set definitions: A = {z € N| (4 < =) A (z < 5)} and B- {{4, 5}} Is the equality A = B true? O Yes, it is true. O No, it is not true. o We need more information in order to decide. Not counting N, are we dealing with two sets or one set in this problem? o One set. O Two sets.

Let N be the set of all ounting numbers: 1, 2, 3,.... Consider these set definitions: A = {z € N| (4 < =) A (z < 5)} and B- {{4, 5}} Is the equality A = B true? O Yes, it is true. O No, it is not true. o We need more information in order to decide. Not counting N, are we dealing with two sets or one set in this problem? o One set. O Two sets.

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

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Two sets or one? Let N be the set of all counting numbers: 1, 2, 3, .... Consider these set definitions: A = {x €N| (2< #) ^ (x < 5)} and B = {2,3, 4, 5} Is the equality A = B true? O Yes, it is true. O No, it is not true. O we need more information in order to decide. Not counting N, are we dealing with two sets or one set in this problem? O One set. Two sets.
Let S be a set of n distinct positive integers, where n is odd. The median of S is the (n+1)/2th smallest number of this set - i.e., the number in the middle of the set once the set is sorted. For example, if S = [70, 10, 20, 60, 30], then the sorted set is [10, 20, 30, 60, 70], from which we see that the median is 30. There is an obvious linearithmic algorithm to determine the median of S. First you sort the set, which takes O(n log n) time. Then you output the value of S[(n+1)/2}, which takes O(1) time. But is this the best we can do? Here is a bold claim: there is an O(n) algorithm to determine the median of set S. Determine whether the above claim is TRUE or FALSE.
As an investor, I always check the stock market in order to find good companies to invest in. Recently, I found that the best companies to invest in, are the ones that have largest sum formed by a strictly increasing set of numbers (a set where the next element is always greater than the current element). But before I invest, I need to know the position of the first element of the consecutive increasing numbers. Help me so we can start investing already! Note: If it is already the last element of the row in the array, the next element is the first element of the next row, if there exists a next row. Input 1. Number of rows Description This is the number of rows of the multidimensional array. 2. Number of columns Description This is the number of columns of the multidimensional array. 3. Elements of the multidimensional array Output The first line will contain a message prompt to input the number of rows. The second line will contain a message prompt to input the…
1. The notation for the cardinality (number of elements) of a set is |A|. For example, for set A = {a, b, c) we can write: |A| = 3 because A has 3 elements. Determine the cardinality of the following sets and explain how you got it: 1. A=(3, 4, 5, 17} 2. B = {n is an Integer | 4 <= n <= 196} 3. C = {n = 2k with k Integer | 0 <= n <= 100} 4. Suppose |X| = 5, |Y| = 5 and IX n Y| = 7, what is IX U YI? 5. Suppose IX = 8, |Y| = 6 and IX n Y| = 6, what is IX U YI?
7. For n 2 1, in how many out of the n! permutations T = (T(1), 7(2),..., 7 (n)) of the numbers {1, 2, ..., n} the value of 7(i) is either i – 1, or i, or i +1 for all 1 < i < n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because 7(3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for 1(n).
Consider the following Tarski world: A C Let W be the set of all things in the world. 14.3x € W, 3y eW, such that (is_Circle(x) V is_ Cinrcle(y)) A is Abovely.x) A. Please provide a reading of the above statement B. Is the statement true or false? How do you know?
In a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English
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What can you say about the set B is equal if we know that: 1- (A U B)= A 2- (AN B)= A 3- (AN B)= ¢ 4- (B – A) = Ā *
You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…
Let S = {1, 2, 3, ..., n). Consider the following two statements: 1. If 12 is odd, then S has the same number of subsets with an odd number of elements as subsets with an even number of elements. 2. If 72 is even, then S has the same number of subsets with an odd number of elements as subsets with an even number of elements. Which of the following is correct? Statement 1 is true and Statement 2 is false. Statement 1 is true and Statement 2 is true. Statement 1 is false and Statement 2 is false. Statement 1 is false and Statement 2 is true.
Let U= {1,2,3,4,5,6,7,8,9,10,11,12}, let A = {4,3,4,7,8}, let B = {7,8,9,10}, and let C = {3, 8, 9}. write down the following set in enumerated form: A ∪ (B ∩ C) Determine the set B X C Write down the set represented by the bit string 110111011011 Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows: R = {(1, 1), (1, 2), (1, 3), (2, 2), (2, 1), (3, 1), (3, 3), (4, 4)} State, giving reasons, whether R is reflexive, symmetric, or antisymmetric.