Question: Use proof by cases to prove that for any integer a, at least one of the integers a, a + 2, and a + 4

Use proof by cases to prove that for any integer a, at least one of the integers a, a + 2, and a + 4 is divisible by 3. (Hint: a must have a remainder of 0, 1, or 2 when divided by 3.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

1. Use the contradiction proof method to prove that if a not divisible b and a | c, then a not divisible b + c,for any integers a, b, and c. 2. Use the contrapositive proof method to prove that if a,...

Last week, we noted that 2n + 3n +n can be factored as the product (2n +1)(n+1)(n). One approach to show that this is always divisible by 3 is to prove that for every integer n, at least one of the...

CSCI 2824 - Spring 2018 This assignment is due on Friday, February 16 either in class or under your prafessors doo by 12 PM (on. Yau are expected to write up your solutions neatly, with ful...

please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove...

You$must$attach$this$cover$page$to$the$front$of$your$HW$or$you$will$lose$5$points.$ $ $ APMA$1860$Homework$2$ $ $ First$Name:$____________________________$$$Last$Name:$______________________________$...

Prove the following statements. A . Prove that the product of two consecutive integers, has the form 3 k or 3 k + 2 for some integer k ( Hint: Your two consecutive integers will look like a and a + 1...

appreciate if you add the source code not just picture Question: Today you are commissioned to create a Java program that will prompt for and read three integers ni, n2 and n3 entered by the user,...

Question: Today you are commissioned to create a Java program that will prompt for and read three integers n1, n2 and n3 entered by the user, and determine the properties of the three numbers...

1 Practice: Another Operation on a Language Define the following operation on languages, OP3, to be: OP3(L)={aabL,b} Give the result of applying OP3 on the following languages (assume strings in the...

Use the method of proof by cases to prove the following statement n3,n23n+3isodd 1.51 Let nZ0. If nmod4{2,3}, then n is not a perfect square. 4.52 Let n and m be integers. If nm is not evenly...

Consider the integral b 1 = (4x + 3x 2). (x 5x+4)dx, where a, b are constants. Which of the following options is/are correct for the different values of [a,b]? For [a,b]= [0, ], I = 79/3 For [a,b]=...

Consider the three linearly separable two-dimensional input vectors in the following figure. Find the linear SVM that optimally separates the classes by maximizing the margin. + +

Question 2 1 ( 3 points ) Miller's Hardware plans on saving $ 4 3 , 0 0 0 , $ 5 5 , 0 0 0 , and $ 5 9 , 0 0 0 at the end of each year for the next three years, respectively. How much will the firm...

CT Corp Comprehensive Question Canadian Tire Corporation, Limited ( Canadian Tire ) is a family of companies that includes a retail segment and a financial services division, among others. The retail...

2-14 What types of information systems and business processes were used by Income before migrating to the fully digital system? NTUC Income (Income), one of Singapores largest insurers, has over 2...

2-10 In this exercise, you will learn how to use spreadsheet software to improve management decisions about selecting suppliers. You will filter transactional data on suppliers based on several...

2-9 Quincaillerie is a small family hardware store in Paris, France. The owners must use every square foot of store space as profitably as possible. They have never kept detailed inventory or sales...