Show the statement below using Zorn's lemma. Let a1, a2, ·.. , an be uniquely different elements of A CR and r1, r2, .· , rn a rational number, then ria1 + r2a2 +…… ri = r2 = .: = rn = 0 +rnan = 0= %3D

Q: Using the formula Ɛijk&mlk Sjk = Skj = - Sim§ji – Siljm, show that ƐijkSjk = 0 for all i if and only…

A: As per the question we are given the relationship between the Levi-Civita symbol εijk and the…

Q: f α and p are constructible, then a ± p, ap and a/p when ß # 0, are also constructible.

A: (i) Since ? and ? are constructible so that (?,?) is constructible. The circle (x-?)2 +y2 =?2 is…

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

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Q: Let 7 be a real number. Which of the following is equal to T T -2 (ED)*+E)* r2 3 0 None of the these…

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Q: Ex(30) and fYx show that of - Ix Exlz0)& Lekf:Xy be fIxYbe be it is

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Definereducible elements. itreducible R and a reducible and in ZuTh7 and sing Aind Irneducible and…

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: O Find the Posifi ve value of * that işfie the egquation x-2X+ 452Bisection methed)

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Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: Evaluate [R(5xy + z²)dV, where B = [-10, 10] × [0, 1] × [0, 10]

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Q: 7. Prove: For neN and F, the nth Fibonacci number, =Fn+1 (1) + (7¹) + ("z ²) + (~³²) +--+ (0) = ² 2…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Given a = (1, 2, 1) and b = (k, 1, 2) and a × b = √35. Determine the ax value(s) of k.

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Q: We know that now 2 1 + d + d +..... :. Since 2 1 + 2k + Zk +.... and 2K be the n 2₁ = 1 2 1+2k + 2k…

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Q: (d) The third quartile for X 提交答案| Tries 0/5 (e) the IQR for X 提交答案| Tries 0/5 (f) P(IX-216|> 41)

A: Given : Let X be a r.v X~N(216 , 18) Here ; μ=216 σ=18

Q: Let A, B, and C are three sets, prove that Bx(AUC)=(B× A)U(B×C)

A: "Since you have posted multiple questions, we will answer the first question. If you want the…

Q: 3. Let a be a primitive 10th root of unity. Which of the following is false? A. a5 = 1 B. a³ = a¹3…

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Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

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Q: DIVISION BYt (:) - {}> 81. Show that In %3D

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Q: For -3-3: (a) Find the modulus and argument of z. (b) Express + in the form of a+ib where a,beR.

A: This is a problem related to complex number. Based on the general concept and formula used for…

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Let Z, = {0,1,2,3,4, 5,6} where each x € Z, is a least residue when an integer is divided by 7. %3D…

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Q: l, tet that 17/2n+3m e integed, prouve iff, 17/9n +5 m and m be

A: Properties used: Property 1. If x divides y, then x divides ky and vice versa. x|y⇔x|ky Property 2.…

Q: If+b+=++, then show that for 1 a" +b" +c"

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Q: 10+1 + 10 + 1 is divisible by 3 for n E N.

A: To prove the given statement we will use the method of mathematical induction in which first we…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.