EXAMPLE: The sum of any two even integers is even.Answer:Proof. (direct) Suppose x and y are even integers. By definition of even, let x = 2k and y = 2j for someintegers j and k. Then,x+y=2k+2j = 2(k + j)Note that k+j is an integer because it is the sum of integers. Therefore, by definition of even, x + y iseven. (d) If x is an integer, then 3x²+5x-1 is odd.

Proof: If x is an integer, then 3x2+5x−1 is odd.Proof (direct):Suppose x is an integer. We will…

Answered: EXAMPLE: The sum of any two even…

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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Similar questions

Two n-digit integers (leading zeros allowed) are considered equivalent if one is a rearrangement of the other (for example 12033, 20331 and 01332 are considered equivalent five digit integers.) a) We need to find the number of five digit integers that are not equivalent. b)We need to find the number of non equivalent five digit integers if the digits 1, 3 and 7 can appear at most once. c) When all three digits (1,3,7) appear once.
find a counterexmaple.
6. Prove: For all integers n, if n² is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1.
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).
n and n+1 are integers with the same number of positive divisions. Find the integers n from 1<n<107. For example, the positive divisors of 14 are 1, 2, 7, 14, and 15 are 1, 3, 5, 15. (P.s.: You have to done it by C++.)
Correct answer will be upvoted else downvoted. Computer science. You are given two integers n and k. You ought to make a variety of n positive integers a1,a2,… ,a to such an extent that the total (a1+a2+⋯+an) is distinguishable by k and greatest component in an is least conceivable. What is the base conceivable most extreme component in a? Input The primary line contains a solitary integer t (1≤t≤1000) — the number of experiments. The solitary line of each experiment contains two integers n and k (1≤n≤109; 1≤k≤109). Output For each experiment, print one integer — the base conceivable most extreme component in cluster a to such an extent that the aggregate (a1+⋯+an) is distinct by k.
make mathlab code
How do I do (K+1)? Please use step by step simply please
(b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3,then n is a multiple of 3. You must do so by a direct proof. For this problem youmay assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xymod m. *Solve by direct proof*
Topic: Proofs (even (2k), odd(2k+1), r = a / b. etc.) Let a and b be rational numbers such that a > b. Then there exists a rational number c such that a > c > b.
What do I do for (K + 1)? Please explain as best as possible
(Please write step by step and cleary, thanks you very much) no hand written

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