Let i be a positive integer and A, = {[.., i – 6, i – 4, i – 2, i, i + 2,i + 4,1+ 6, . ). Then N 4 %3D

Q: Let i be a positive integer and A =] - i+1,1]. Then N1 A O 10,1[ O 10,11 O 10,1] O None of these

A: ]0, 1] is correct

Q: 14. Let (a, b) = 1 and 2 = y for some integers x and y. Then prove that there exists an integer n…

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Q: (a) Prove that 3n2 +1 is even if and only if n is an odd integer. (b) Suppose A, B,C and D are sets.…

A: The given question has two parts. The solution is explained below.

Q: Let i be a positive integer and A, = [-i+1,1]. Then U, A O R O 1-0,1] None of these -1,1]

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Q: A. Prove that for all positive natural numbers n, 13 + 23 + . + n³ = n²-(n+1)²/4. + ...

A: Explanation of the answer is as follows

Q: 11. What is the sum of all possible positive integers a, such that for any positive is an integer?…

A: Claim: n(n+2)(n+4) is always divisible by 3. Proof: we know, n = 0 or 1 or 2 (mod 3)    When, n = 0…

Q: Let a and b be two integers such that b | a. Let p be a prime such that p|a and p{b. Prove that p|…

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Q: Given positive integers k and m, there exists an integer N ≥ m such that N →(m)k

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Q: Let n ≥ 1 be an integer. Show that in any set of n consecutive integers, there is exactly one that…

A: According to the given information, it is required to show that in any set of n consecutive integers…

Q: Let i be a positive integer and A; =] - i+1,1 [. Then N A= None of these O 10,1] O 10,1[ [0,1[

A: Ai = ] -i+1, 1 [  A1 = ] 0, 1 [ A2 = ] -1, 1 [ Thus ∩Ai = ]0, 1[

Q: Let n be a positive integer. Prove that (:) () (:) 1. 1 + 2. 2 +n n2"-1

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Q: Find all integers n such that n| (2n+3). *

A: Given, n|(2n+3)     TO find, All integers n

Q: There are 51 software students taking MATH 211. Let p1, P2, ..., P51 be their final exam scores.…

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Q: If n > 2 is prime then n | a"-1 1 for all positive integers a with gcd(a,n) = 1. Select one: O True…

A: True

Q: 10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a2" +1…

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Q: Let a = 1, and let an+1 4a, – 1, for all nonnegative integers n. Prove that an 2-1"+1 3 %3D

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Q: For all n E N,n > 1, there exists a prime p such that p|n. ulgn hi

A: False

Q: 1. Let, a1 = 7 and for n > 2, an = "1 express an in terms of n.

A: According to our guidelines, we can solve only the first question. Please repost other questions as…

Q: Let i be a positive integer and A, = {.., i – 6, i – 4, i – 2, i,i+2,i+4,i+6,.. ). Then NA= O set of…

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Q: Let an m be non-negative numbers for all integers n, m > 0. Deduce Ši an,m = ΣΣ An,m n=0 m=0 m=0 n=0…

A: according to fubini's theorem if am,nm=1,n=1∞ is a doubly indexed sequence of real number then we…

Q: Let n be a positive integer. Prove that (:) n +2. +...+n. n2"-1.

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Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

Q: all integers h, k, and with

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Q: Use the permutation and combination formulas to prove the following. (a) For all integers n 2 2,…

A: We will solve the problem

Q: How many 2-permutations are there of a set of eight objects? Prove that for all integers n > 2, P(n…

A: The formula of permutations is given as nPr = P(n, r) = n!/(n-r)!

Q: If a and b are positive integers such that gcd(a,b)=13, then find the sum of all possible distinct…

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Q: (a) Show that if x E Q is such that |x|, < 1 for all prime numbers p then x E Z.

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Q: 59. Let N be the set of positive integers and for each k € N, let Ag = |0 ,2- Find U-1 Ak- =D1 А. 0…

A: Let ℕ be the set of positive integers and for each k∈ℕ, let Ak=0,2-1k

Q: 1 If n is a positive integer, then (D-a %3D n!

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Q: Show that for any r, n > 1, п! Σ = r". nį!n2!...n,! nį+n2+…+n,=n, n¡ 20 11 (

A: Given information: The sample size is n. The number of categories is r.

Q: Find an explicit formula for an if a0= 1, a1= 2, and an= 2an−1−an−2for n ≥ 2.

A: given a0= 1, a1= 2  and an= 2an-1−an-2for n ≥ 2.

Q: 9. (a) Show that if n is an integer, then: -o3* (") = 4". %3D (b) Let n be a positive integer. Show…

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Q: Let a1, a2,⋯, a2021 be positive integers. Prove that there exist at least two different sequences…

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Q: Show that if n is a positive integer, then k+4 n(3n +7) k(k +1)(k+2)¯ 2(n+1)(n+2) k=1

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Q: Let n be a positive integer. n+1 n+1-r (a) Suppose r is an integer amongst 0,1, - n. Prove that…

A: as you have specifically mention only first part i.e. 2)a) here is the solution.

Q: Let i be a positive integer and A; = {..., i – 6, i – 4, i – 2, i, i + 2, i + 4, i + 6, ... }. Then…

A:

Q: 3. Prove: For all positive integers, n, n(n + 1)(n + 2) >i(i + 1) = 3

A: Kindly find the attachment

Q: Let i be a positive integer and A, = {..., i – 6, i - 4, i – 2, i, i + 2, i+ 4, i + 6, ... }. Then…

A: First option is correct

Q: Let i be a positive integer and A; =] – i + 1,1 [. Then N, A;= O [0,1[ Ø O 10,1[ O 10,1] None of…

A: Intersection of sets which are forming ascending chain(i.e. A1 contained in A2, A2 contained in A3,…

Q: Let i be a positive integer and A, = [-i+1,1[. Then N14= %3D

A: We have to find the first intersection first.

Q: Prove, for all positive integers n, 1 3 2n – 1 1 2 4 2n V3n

A: For all positive integers n, we need to prove that, 12·34···2n-12n&lt;13n

Q: Let i be a positive integer and A; = [1,i+1[. Then U A OR O [-1,1] O [1, [ O 11, [ None of these

A: [1,inf[ is correct answer

Q: Find all positive integers n such that p(n)|n.

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Q: Prove: Let a,b,x and y be integers. If a|x and b|y then (ab)|(2xy).

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Q: Let i be a positive integer and A; = [1,i+1[. Then U2, A= O [-1,1] O R O 11, [ O [1, [ None of these

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Q: Let i be a positive integer and A, = {., i – 6, i – 4, i – 2, i, i + 2, i + 4, i + 6, ... }. Then…

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Q: Let i be a positive integer and A, = [-i+1,1[. Then N2, A,- None of these O 10.11 [0,1[ 10.10

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Q: 2. Find a positive integer a such that 4 | a, 9| a+ 1, and 25 | a + 2.

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Q: Let i be a positive integer and A; =[1,i+1[. Then U A;= O [-1,1] O R O 11, [ O [1, [ None of these

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