integers a and b, if a^2+b^2 is odd, then a or b is odd.    use indirect or direct proofs    discrete math

Q: Sum of two different prime number is a Prime number None of the mentioned o Either Prime or…

A: Given, Sum of two different prime number is a ______

Q: College Geometry (Proof):State whether the following statements are correct or not:Give a short…

A: The question comprises multiple parts. Here, I will be answering the first question only, that is…

Q: Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2). Also…

A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

Q: State whether each conjecture is true or false.Give a counterexample for any false conjecture. For…

A: False.    conjecture. For all number x, x4 > x

Q: Serial numbers for a product are to be made using 3 letters followed by 4 digits. The letters are to…

A: The serial number for a product are to be made using 3 letters followed by 4 digits. The letters are…

Q: What method do we use to prove the statement: Vinteger n, 5" - 1 is divisible by 4. Direct proof…

A: We use Mathematical Induction. Let's start For n = 1   5 -1 = 4 is divisible by 4. It is true for n…

Q: 5, 11,17,. Find the 35th term.

A: We can use the Arithmetic progression In order to solve the given problem.

Q: Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to…

A: Number of possibilities: Here, the password consisting of 2 letters followed by 2 digits. There are…

Q: Prove or disprove formally and precisely that the product of two consecutive integers is always even…

A:

Q: randomly selected. Thus, the robability that this number be one of 8 multiple is

A: A number of two digits is randomly selected. The number is multiple of 8

Q: elect any two-digit number. Multiply it by 9 . Then add the digits. Keep adding the digits in the…

A: case-i according to question  step-1  select any two digit number let the two digit number be 74…

Q: indirect proof? of that can only use num

A:

Q: 5. (a) Show an exemple of a proof or computation that uses the FTOC part 1. Make sure to the label…

A: Fundamental theorem of calculus part 1: Let f(x) be a continuous function on an interval a, b. The…

Q: 7. If x is a positive prime integer, then x+7 is a composite integer. (i.e., not prime)

A:

Q: How do I prove that 1 is the smallest natural number by using Axiom of Induction & the well ordering…

A: Well ordering Principle states that " every non empty subset of a well ordered set has a smallest…

Q: ropriate algebra and Theorer s + 4s - 5,

A:

Q: State whether or not the following are statements. In the case of a statement, indicate if it is…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Differental Equafions Ex: 9メ-69=。

A:

Q: prove that the sum of three odd integers is odd using indirect method. show your solution and…

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Q: Let A2A2 be the set of all multiples of 2 except for 2.2. Let A3A3 be the set of all multiples of 3…

A: Let A and B be two sets. Then the union of two sets will be the set that will contain all the…

Q: Describe the methods of proof by induction and proof by contradiction.

A: The main objective is to describe the methods proof by induction and proof by contradiction. The…

Q: Serial numbers for a product are to be made using 2 letters followed by 4 digits. The letters are to…

A: There are 7 letters and 10 digits. It is required to obtain a serial number with 2 letters and 4…

Q: (uA)ū and u(Av) as sums of products of the entries

A: Note: Here we are solving problem 5.a) for reaming problem please submit the question again. Given:…

Q: "When proving a complicated theorem, it can help if we propose and prove one or more first, using…

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Q: x + 2 2 2 ()--()+ () nat there exists at most one ing x +1 + (2.

A: Consider the given function: φ(x)=φx2+φx+12-φ12

Q: do i prove this

A: Introduction: A triangle could be a 3-edged polygonal shape with three vertices. it's an elementary…

Q: (2) Conjecture a formula for the number of sub- sets of an n-set and prove it by induction.

A: Conjecture a formula for the number of sub-sets of ann-set and prove it by inductionIf S is any set…

Q: A person has coins consisting of quarters, dimes, and nickels. If the person has (or aim to have)…

A: A nickel is worth 5 cents. A dime is worth 10 cents. A quarter is worth 25 cents. Let the number of…

Q: Serial numbers for a product are to be made using 2 letters followed by 3 digits. The letters are to…

A:

Q: To prove the Well-Ordering Principle, we need to assume the truth of which one of these principles?…

A: The well-ordering principle says that the positive integers are well-ordered. An ordered set is said…

Q: A password for a website consists of 5 characters. The first 2 characters are digits. Theother 3…

A: The first two characters of the password are digits and the last 3 characters are uppercase letters.…

Q: Determine whether the statement is true or false. Modify each false statement to make it a true…

A: A number y is said to be divisible by another number x if we are able to divide the number y with x…

Q: proving card{Q} = card(QU{e,pi,sqrt(2)}) and also if A1,A2,A3 .... is countable, then The infinate…

A:

Q: 8.) Write a conjecture using the information provided. If two numbers are odd, then their sum is…

A: The information provided is that,  If two numbers are odd, then their sum is even. We note that 3…

Q: .Prove that if n is an odd number then 3n + 1 is an even number. Use direct proof. 2.Prove that…

A: Given n is odd number

Q: There are three natural number that are less than one thousand that are both perfect square and…

A: Consider the first ten cube numbers 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. Check how many…

Q: Prove using direct proof. Include explanation.   If n is an even integer, then 7n + 4 is an even…

A:

Q: In ________________ draws from the box, there is more than 50% chance for a red marble to appear at…

A: Here Given  No of red marbles=2 No of Blue marbles=98

Q: A property that, two consecutive positive integers are relatively prime. Consider any two…

A: Proof) Let the consecutive integers be n,n+1 Let the greatest common divisor gcd(n,n+1) = d, Hence,…

Q: medium second and another arrangement is medium first, large second. How many such arrangement are…

A: Hezekiah has six boxes of six different sizes. Four box are taken at a time and arrange in definite…

Q: Serial numbers for a product are to be made using 2 letters followed by 4 digits. The letters are to…

A: Givenserial numbers for a product are to be made using 2 letters followedby 4 digitsNo.of letter = 8…

Q: Can 199 cannot be written as the sum of an even integer and two odd integers. Show prove too.

A:

Q: Prove the divisibility criterion of 2 and 13

A: Divisibility Criteria for 2: Any integer is divisible by 2 if and only if unit digit of the integer…

Q: Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest…

A: Given that, A numver is, 2n - 1 Where n = 2, 3, 4, 5, 6, 7, ............ We have to find the…

Q: Q1 Prove thet if seven distinct numbers are selected from {1,2,. 11). then some two of these numbers…

A: “Since you have asked multiple question, we will solve the first questionfor you. If you want any…

Q: For all nteges a, if 615a, then 6la.

A: any integer which is divided by 2 and 3 that implies it is divided by 6 also.

Q: le sum of any two green Rewrite the statement wit What are the hypotheses of What is the conclusion…

A: Given the sum of any two green  numbers is a blue   Let  x and y be any two green numbers   x+y is a…

Q: 4. An informal proof uses to show that a conjecture is true. O specific examples geometry rules…

A: Given that to show a conjecture is true

Q: Prove the 8 divisibility test for ANY number. This should be a mathematical proof, not a word or…

A: Suppose a number with digits abcd can be expanded as1000a+100b+10c+d…

Q: "") = (n-k) (") k<n %3D

A: