Q: Abstract Algebra. Please explain everything in detail.
A: To prove (or disprove) the possibilty of required representations under the given conditions
Q: 1. Let y be a positive real number. Prove that for every n e N there exists a unique positive real…
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Q: 5**) (a) Prove that for all positive real numbers n, r, and s, if rs < n, then r < Vn or s < Vn.
A: As per Bartleby's answering policy, we can answer only one question, so kindly post the next…
Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(A U B)…
A: Let A,B not empty, bounded subsets of R .Prove thatsup(A∪B)=max{sup(A),sup(B)}. Let: ⇒x∈A∪B⇒x∈A or…
Q: Note that 1/4 ≠ 1/2; but (1/4)^(1/4) = (1/2)^(1/2). Use the hint "y = x^x" to prove that there…
A: Please check next step for details.
Q: Let A be a nonempty subset of positive integers and B = {n + v5 : n E A}. Show that B has a least…
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Q: Prove that for all integers a,b which are not both 0, and for all integers d, d|gcd(a,b) if and only…
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Q: If r and s are real numbers and r < s, then there exists a positive integer t such that r+t = s.…
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Q: Let n > 3 where x, y , z € R", |x – y| = d > 0, and r is some positive real number. Prove that if 2r…
A: It is given that x and y are d distance apart and r>d/2 where x, y, z belongs to Rn So locus z…
Q: Let a, b eN. Prove that if a + b is even, then there exists nonnegative integers x and y such hat x²…
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Q: Let x and y be integers. Prove that if x2 + y2 is odd, then x+y is odd
A: Given x and y be an integers. We have to prove that if x2+y2 is odd then x+y is odd. Since given…
Q: Let a be an algebraic integer in Q(v-37) and let A = (2, 1 + v-37). Prove that either a or a –- 1 is…
A: Given that, α is an integer in Q-37 lets consider α=-37⇒α-1=-37-1
Q: Let x,y,z∈ Z be integers. Prove that if x(y+z) is odd, then x is odd and at least one of y or z is…
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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: 4. Let R be the set of all real numbers, xER and n EN such that n 2 2. If (1+x) > 0, prove that Pn:…
A: Let ℝ be the set of real numbers, x∈ℝ and n∈ℕ such that n≥2. If 1+x>0, we want to prove that Pn…
Q: 4. Let D (d,}neN be a set of real numbers satisfying d,41 2 d, +1 for all ne N. Prove that D is an…
A: Let D = { dn }n in N be a set of real numbers satisfying dn+1 >_ dn + 1 for all n in N. Then, we…
Q: Prove that there exists irrational numbers r and y such that x" is
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Q: For every pair of integers x and y, if x – y is odd, then x is odd or y is odd.
A: Let x-is even integer and y-is even integer. x=2m, y=2n
Q: Prove that there are integers x and y such that 10x-13y=1
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Q: Assume B is a closed subset of the real numbers. Prove that Bc = R−B is an open set.
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Q: (5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x…
A: To prove: If x is any real number and any subset A of ℝ, then either x is an interior point of A or…
Q: For all positive integers a, b, where a < b, if gcd(a, b) = 1, then a b. O True O False
A: " Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: If α is even, prove that α-1 is even. If α is odd, prove that α-1 is odd.
A: We know that the multiplication of 2-cycles can help us find any permutation of a finite set, so we…
Q: Let {x1, x2,..., xn} C R be a subset of real numbers. Prove that (x1 + x2 + . + an)² < n(x² + x +·.…
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Q: Prove that if S is dense in the real numbers, and I = (a, b) is an open interval, then I contains…
A: Prove that if S is dense in the real numbers, and I = (a, b) is an open interval, then I contains…
Q: Prove: Provided it exists, (A-1)¯ = A.
A: Hey, since there are multiple questions posted, we will answer first question. If you want any…
Q: In the set R of real numbers, define C, = (n,n+1) = {xeR|n < x <n+1} for each integer n. Determine…
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Q: To be onto, for any integer y, there exists an integer x such that y = f(x). Give a counterexample,…
A: To be onto for any real number y, there exists a real number x such that y = f(x). Let y be a real…
Q: Let a and b be any real numbers such that a 0. Prove that a < b.
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Q: If x and y are two positive real numbers, then there exists a positive integer n such that ny>x
A: Proof: Suppose there does not exist any positive integer n such that ny>x then ny≤x ∀n∈ℕ
Q: There exists two odd integers whose average is odd. 1 1 1 There exists distinct positive integers a,…
A: (a) Consider two odd integers 2m+1, 2n+1 such that m+n is even. Now, Consider the average of the…
Q: Provide a proof by contraposition of the statement below. Prove that for any integer æ, if x + x +1…
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Q: Assume A is an open subset of the real numbers. Prove that Ac = R−A (the complement of A) is closed.
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Q: Let a be any positive number. Prove that |x| >a if and only if x > a or x < -a.
A: Suppose
Q: Prove that for any integers N and m, the set 1 x + m 1 {x € A : \x| < N, and (x inA = {x}} | m…
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Q: 4. Let R be the set of all real numbers, xER and n E N such that n 2 2. If (1+x) > 0, prove that P,…
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Q: 4. Let R be the set of all real numbers, xER and n EN such that n > 2. If (1+x) >0, prove that Pn :…
A: Mathematical induction.
Q: Consider the subsets ø (empty set) and R of the real numbers. Prove that both of these are open and…
A: Consider the set of real numbers ℝ. We know that a subset A of ℝ is open if for every x∈A, there…
Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(AB) =…
A: Suppose A and B are bounded and nonempty subsets of real numbers and λ∈R. We need to prove that…
Q: Prove or disprove: The set {0, 1} × R is uncountable, where R is the set of real numbers.
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Q: Prove that e" > x+ 1, for all positive real numbers a.
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Q: Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x is an…
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Q: {p € Z :x | p}U{p € Z:y|p} C {p € Z :n| p}. : n
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Q: Let x, y and z be real numbers. If x > y and y = z, then x > z. For any real numbers x and y, with x…
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Q: True or False? If d = gcd(a,b), then there exists integers x, y such that d = ax +by
A: solution.
Q: Let A be a nonempty subset of positive integers and B = {n + v5_ : nE A}. Show that B has a least…
A: We will use the well ordering principle to prove that B has a least element.
Q: Prove the following statement using the axioms and lemmas For all nonzero real numbers w, x and y,…
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Q: Prove that for all real numbers x, if x is not an integer, then [r – 1] = [x] – 2.
A: We have to prove x−1=x−2 for all real number x, if x is not an integer. Use definition:- x is the…
Q: Let x and y be coprime positive integers. Prove gcd(x + y, x² + y²) E {1, 2}.
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Q: Prove that if m is a positive integer and x is a real number, then [m2] = [=] + z++ + 2 + |x + т — 1…
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- Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 3% of the microprocessors produced by firm A are defective, 4% of those produced by firm B are defective, and 1.5% of those produced by firm C are defective. Firms A, B, and C supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
- In 1940, a county land-use survey showed that 10% of the county land was urban, 50% was unused, and 40% was agricultural. Five years later, a follow-up survey revealed that 70% of the urban land had remained urban, 10% had become unused, and 20% had become agricultural. Likewise, 20% of the unused land had become urban, 60% had remained unused, and 20% had become agricultural. Finally, the 1945 survey showed that 20% of the agricultural land had become unused while 80% remained agricultural. Assuming that the trends indicated by the 1945 survey continue, compute the percentages of urban, unused, and agricultural land in the county in 1950 and the corresponding eventual percentages.The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare Southwest Airlines flights, 35% are US Airways flights, and 25% are jetBlue flights. a) Deveiop a joint probability table with three rows (airlines) and twoKentville, a community of 10,000 people, resides next to a krypton mine, and there is a concern that the emission from the krypton smelter have resulted in adverse effects. Specifically, Kryptonosis seems to have killed 12 of Kentville’s inhabitants last year. A neighboring community, Lanesburg, has 25,000 inhabitants and is far enough from the smelter to not be affected by the emission. In Lanesburg, only three people last year died of Kryptonosis. Given that the number of deaths in Kentville and their causes last year were: Heart attack=7 Accidents=4 Kryptonosis=12 Other=6 What is the risk of dying of Kryptonosis in Kentville relative to non-contaminated locality?What is the risk of dying of Kryptonosis in Kentville relative to deaths due to other causes? How many times the chance of dying of Kryptonosis compared to dying of accidents ? How many times the chance of dying of Kryptonosis compared to Other causes?
- To determine the effectiveness of an oil additive, a testing firm purchased two cars of the same make, year, and model, and drove each a distance of 30,000 miles using the same kind of gasoline, the same kind of oil, the same driver, under the same road conditions. The oil in one engine included the additive, whereas the oil in the other engine did not. At the end of the test, the engines of both cars were dismantled, and it was found that the engine that contained the additive had less wear. The testing firm concluded that the oil additive caused the reduced wear.A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations. a. If 15 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of atleast one regulation? b. If there are 500 firms in the area, of which 150 are in violation, approximate the pmf of part (a) by simpler pmf. c. For X = the number among the 10 visited that are in violation, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b).Suppose that 15% of a Canadian wholesaler’s food products are gluten-free. Furthermore, 70% of its products are peanut-free. Assume that the use of nuts and gluten-containing products are independent. 1. (a) What percentage of this wholesaler’s products contain at least one of the two allergens? (b) What percentage of this wholesaler’s products are allergen-free? 2. What percentage of this wholesaler’s products contain peanuts but no gluten?
- plz provide handwritten answer for question 4 part c asap for getting upvoteAt a company, the quality assuran_ce staff has set up a criter_ion to assure if the quality of their products are ready to be expor_ted. Each of the exported box contains 25 pieces of their product. Three inspection staffs are assigned to do one by one inspection. Namely, the first inspector will randomly select one piece from the box and record if it is defective or non-defective and return that piece to box. The second inspector has repeated the same way of inspection as the first inspector and, lastly, the third inspector also repeats the same action one more time. The criteri_on is as follows. If all inspectors have not found any defective product, then {th_e} box is accepted to be exported. On the other hand, if at least one of the inspector has found the defective product, the whole box must be rejected and must be returned for reproduction. By considering this way of inspection process, find The prob that a box contaning exact_ly 3 defective product would pass the inspection…A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d below