Let 9={a: aER}, then T is Borel algebra.

Q: Let G= Z* and let * be an operation in a * b. Is a * b = ab/2 is closed under the operation?

A: Disproof by an example.

Q: Q3 Iet X-{mingP;q } and ΦΧ 3. min is 2 asigma algebra over over X ?

A: Given that  X = {m, n, p, q} and ∑=ϕ, X, {m}, {n}, {p, q}, {m, n}, {n, p, q}, {m, p, q} we have to…

Q: Let J={a: aER}, then I is Borel algebra.

A: False Statement' Detailed Explanation

Q: Consider the ODE system x' = A et + 3 with A = 4 1 3 a) Use the method of diagonalization to find…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Let 7={a: a€R}, then 9 is Borel algebra. ylgn ihi

A: True

Q: If El and E2 are sigmas algebras over X, is ElU E2 are sigma algebra over X? Prove your answer.

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Q: be a field and let c,d e F. Show that c · (-d) = -(c d).

A: Associative Property of Field F for a,b,c∈F a·b·c=a·b·c

Q: = a . Let S = { la, b e R} and let p:S → R be defined by : Ø( D 1) is a ring

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A: Given problem:-           A∪B∩C=A∪B∪C

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Q: In Qu, finot dehrmone the numben and then find all the Conjugate g j .

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Q: Let a E R which expressions are correct? and give the justification why they are part of the Borel o…

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Q: Part Ca):- a*t a e CCR) for all ae R sthen prove that R is commutative.

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Q: 3. How many units are in the ring (Z/15Z) × (Z/125Z)?

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Q: 2. Prove that if 5BA+ ACA – I = A, then A must be invertible.

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Q: For each matrice A, show for definition norm A we can write: |A| + -1

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Q: : which of the following are inner product V, CR) where u = (al1,Ne] , V= on 2

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Q: Let a ER which expressions are correct? and give the justification why they are part of the Borel…

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Q: On R, which of the following is a a- algebra? 1. R. 2 -n, nl; n e N}. 3. P(R). 4. {{x};x€ R}. 4

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Q: Let A; be elements of T for i E I. Show that Uiel A¡ E T.

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Q: Use membership table to prove (AunionB) – C = (A – C) union (B - C).

A: We need to prove the following statement using membership table. A∪B-C=A-C∪B-C

Q: Let T={[a, ) : a€R}, then T is not Borel algebra.

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Q: Let a ER which expressions are part of the Borel o algebra, B(R) they are correct? and give the…

A: The main objective is to determine the correct option.

Q: Given the bases B = {u,u2} and B'= {u', u'2} for R?, where and u'= The transition mat rix Pg-g' from…

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Q: Prove that if gcd(a, b) = 1 and gcd(a, c) = 1, then gcd(a, bc) = 1. %3D

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Q: 7. Let B =- and = are bases for R? %3D

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Q: Let 9={[a, ): a€R}, then T is not Borel algebra. ulgn O ihi O

A: Solution  False Detailed Explanation

Q: Let T={(a, 0): aER}, then T is Borel algebra.

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Q: Prove Theorem  A + (B + C ) = (A + B ) + C .

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Q: Let T={(a, o): aER}, then T is Borel algebra

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Q: eces. To form a le, so that the a

A: It is given that, a wire of length 20 feet is cut in to 2 pieces. X+Y=20 Here, X=2πr is the…

Q: Find the representation B of L with respect to S' and T'.

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Q: (u, v) is an inner product. Prove that the given statement is an identity.         <u + v, u -…

A: Given : (u,v) is an inner product . Use here some properties of inner product  <u, v>= uv…

Q: Let A be a diagonalizable 3x3 mat rix with P AP = -I, where I is the identity mat rix. Which of the…

A: Option D; A=-I is false.   Theorem: Finding the matrix D which is a diagonal matrix and which is…

Q: Let J={(a, ∞ ) : a€R}, then T is Borel algebra. ulgn O

A: Given a statement

Q: Let K = Span{ t-t, 1+3t}, then dim K = %3D

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Q: e) proj(a onto b)

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Q: Let T={a: aER}, then T is Borel algebra.

A: Given a statement

Q: Consider the bases B= {(3, -1), (1, 1)}, B'= {(2, 5), (1, 2)}, and S= {(1,0), (0,1)} of R'. If [u],…

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Q: Let A EMn (R) be given. If 11x11 = 11yll = 1 and x •y = 1, show that x=y

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Q: Let J={(a,∞): a€R}, then T is Borel algebra. صواب İhi

A: True

Q: Let A = {x E Z* : x is a mutiple of 2 and x < 15}. Rewrite A in roster notatlon.

A: Given that : A = {x∈Z+ : x is a multiple of 2 and x &lt;15 }   Roster form : A representation of a…

Q: Consider the standard topology on R, Let A=[3,7], the interior of A is Oa A O b.6 Oc. (3,7) OdR

A: Consider the standard Topology on R. Given A =[3,7] We need to find the interior of A.