Tutorial 5 (Methods of Proof)1. Proof the following statement:2.Ia) Let x E R. If x > 0, then x² + 2 > 0b) Suppose ne Z. If n² <0, then n is positive or negative number.c) Proof that 5X + 3 is even if and only if X is odd.d)Prove the following sentence using Proof by Contradiction technique.For all real numbers x and y, if x + y >= 2 then either x >= 1 or y >=1.Let n e Z. Then n²+ 3n +5 is an odd integer (PROOF BY CASES)B7261%

1. Proof the following statement: I a) Let x E R. If x > 0, then x² + 2 > 0 b) Suppose n € Z. If n² < 0, then n is positive or negative number. c) Proof that 5X +3 is even if and only if X is odd.

1. Proof the following statement: I a) Let x E R. If x > 0, then x² + 2 > 0 b) Suppose n € Z. If n² < 0, then n is positive or negative number. c) Proof that 5X +3 is even if and only if X is odd.

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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53. What is the value of x if:x>>2=2 a. 8 b. 4 c. 2 d. 1
21. The five line bellow are used to determine the profit or loss of a sale based on the buying cost and selling result after a margin calculation. The correct order of the program is . 1n = int (input () ) 2 buycost - 1000 * n + 1000 3 sellResult - 1200 • n 4 if (sellPrice-buyPrice>0) : profit = True if (sellPrice-buyPrice<=0): profit = False 6. a. 1,2, 3, 4, 5, no line of code can be reversed b. 1, 2. 3, 4, 5. with line-1, line-2, line-3 can be reversed each other c. 1, 2. 3, 4, 5. with line-4 and line-5 can be reversed with line-6 and line-7 d. Line-4 untul line-7 must be in sequence but can be placed in any order
Q.2: Simplifying the following with the help of Boolean algebra Rules: (а) А ВС + АВ С+ АВС + АВС + АВС (b) АВ С + А В С +АВС +А ВС
Given two integers, a and b, return true if a can be divided evenly by b. Return false otherwise. Examples divides Evenly (98, 7) true // 98/7 = 14 → divides Evenly (85, 4) false // 85/4 = 21.25 → Notes a will always be greater than or equal to b.
3) Define the variable x as x=6, then evaluate: a) x'+ 2x - 11 b) (x – 2) ² – 8 (x- 2) * c) 4
a) Given the following codes int x = 0; int *y = while(x < 10) { int z = 0; 1: 2: 3: 4: 5: 6: 7: malloc(sizeof(int)); int y = x; while (y } < 10) { z = z + y; y = y + 1; 8: 9: 10: } 11: *y = x; Write the symbol table indicating the type of variables in line 4
In the question below suppose that Q(x) is “x + 1 = 2x”, where x is a real number. Find the truth value of the statement. ∀xQ(x)
3. Spirometry is a test of lung function that measures how much and how quickly (volume and flow) the air movement in and out of the lungs. The measurements are made using an instrument called spirometer, which can provide the following parameters: i. Forced expiratory volume in one second (FEV1) ii. Forced vital capacity (FVC) These parameters can be used to make a diagnosis and to determine the severity of chronic obstructive pulmonary disease (COPD), an obstructive respiratory disorder characterized by airflow limitation and inflammation. It happens when the ratio of FEV1 to FVC is less than 0.70. The spirometric classification of COPD severity based on FEV1 is given in Table 5. Table 5. Spirometric classification of COPD severity. Condition / Severity Normal Mild COPD Moderate COPD Severe COPD Very severe COPD FEV1/ FVC > 0.70 FEV1 > 0.80 0.50 –- 0.79 < 0.70 0.30 - 0.49 <0.30 You are required to develop a program used by a medical practitioner to analyze the condition of few group…