complex numbers then prove that If a, az, . . ..a, and b,, b, . .., b, are |a,5, + a,b, + ..+a̟ b̟² s (l a,f |+| a,f + ...+|a,) (l b,P +|b,² + .

Q: Let U = {1,2,3,4,5), A = {1,3,5}, B = {1,3,4), and C = {2,3,5). (a) Find A U (BUC). (b) Find (AUB)…

A:

Q: 56. Find U₁A, and A; if for every positive integer i, a) A = {i, i+1,i+2,...}. b) A, = {0, i). c) A₁…

A: According to guidelines we can solve only first three subparts.

Q: Prove the following statement: 22 +23+24+... 2n+1 = 2n+2-4

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Q: U = { all real numbers} A = { 10, 11, 12, 13, 14, ...} B = {-3, -2, -1, 0, 1, 2, 3} C = {-1, -2,…

A: This is a problem related to set theory. Based on the general formula we will answer the question.…

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: Given- Ω=set of all real numbers  A= index set  To identify the generalized union and intersection…

Q: coprime

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Q: 1 2 5. 2 . 5 +1. Va) da Find + C

A: Given: I=∫-5·x6+1x-2x6+1·xdx We know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: 27 | 25n+1 + 5n+2, (d))43|6"+2 + 72n+1.

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Q: z = (a + bi)4n+ (b + ai) 4n; a ∈ ℝ ; b ∈ ℝ; n ∈ ℕ. Show that z is a real number.

A: Properties of complex number : If z is real number than z=z¯ . Suppose z=x+i y than z¯=x- iy .…

Q: Suppose x and y are integers. Show that If x y, then x | 3y - y + 5y. 1) What is your assumption? 2)…

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Q: -1 -2 -3 -41 1 2 3 Let A = 1 2.) Find adj (A)

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Q: 4 9 5- .2 13) =D1 7 2+-+ X x²

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Q: 4. Knowing that 1 + 3 + 5 + …+ (2n – 1) = n², find 1++3 +5 + .…+ 135 =

A: Solution :   Given that  1 + 3 + 5 + ... + (2n - 1) = n2    -----(1)

Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

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Q: (a+b)(a+ba)(ao³ + bw) = a' +b*

A: The question is wrong. Ask your guide for correction.

Q: Which of the followings are false? I. General term of {2,3,2,3,...} is an =;+(-)". . General term of…

A: The details solution is given bellow.

Q: (A1+A2+A3+ +An)" = a) Af + A + A +..+ A b) A +A1+.+A + Af n-1 c) A+ A 2+.+ A + Af d) A + A-1+ .+ A +…

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Q: 51. Find U A¡ and A¡ if for every positive integer i, a) Aj = {-i, -i + 1, ., –1,0, 1, . , i – 1,…

A: 51) i be a positive integer so  i ∈ 1,2,3,4,......a) Ai =-i,-i+1,.....-1,0,1,.....,i-1,iA1 =-1,0.1 ,…

Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

A:

Q: EIf a,,a,,a,.--,a, be an A P of non - zero terms, prove that ------ 1 1 +. 1 n-1 %3D a,a, a,a, a,a,

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Q: Prove that for all real numbers Ex)y= -(1u)

A: We have to prove that for all real numbers (- x)y= - (xy)

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 172n-3 ac? E13 cn 4 с — В

A: SUm of infinite terms of G.P. isa1-r

Q: II. Let Q-set of all real numbers, A-index set. Identify the generalized union and intersection of…

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Q: EIf a,,a,,a,,...,a, from an A.P. with common difference d, then prove that : а,а,а, а,а, а, а,а,а, ,…

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Q: .Prove that la + b + c| < |a] + |b| + ]c]

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Q: Let X= a, b, c, d, and classify each of the following as -algebra or not justifying all your…

A: Here X = {a, b, c, d}    Any collection à of subsets of X is a σ-algebra if it satisfies following…

Q: Let a, b, c be integers. Prove that if a|b and a|c, then a|(b +c).

A: Suppose a|b and a|c. Then there are integers m and n such thatb = am and c = an.Then b + c = am + an…

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

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Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…

Q: (Prove that A (B-A) = by stating all laws

A: