Q. If 2, and , are segma algebras over X, En E, is a sigma algebra over X b. E,uE, is a sigma algebra over X 2,\2, is a sigma algebra over X d. None of these. а. '2 C. 2) WWW

Q: 5. Show that M:= {ECR: E is countable or E is countable} is a o-algebra.

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Q: Q. If E, and E, DU is a sigma algebra over X Σ are segma algebras over X, a. (2 b. En E, Σ is a…

A: b. ∑1∩ ∑2 is a sigma algebra over X

Q: (a) Pieve that f 2 and Ź are segma algebras s over X th

A: Definition of Sigma Algebra: A Collection ∑1  of subsets of an arbitrary algebra if : (1) X ∈∑1…

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: J1 Q2. (a) Prove that ifE, and >, then nE, is a sigma algebra over X. (b) Is ,u, a sigma algebra…

A:

Q: the base of an objec cross sections (perper nd your answer to at

A: Here, in the question, the graph shows the base of an object. We have to compute the value of the…

Q: Q2. (a) Prove that if , and E, are segma algebras over X, then . Σ is a sigma algebra over X. (b) Is…

A:

Q: True

A: False.

Q: How do you derermine of RS → R* 76 onto?

A:

Q: Prove that in a Boolean Algebra, x.ỹ = 0 if and only if x. y = x .

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Q: Let U, A, B, and C be defined as shown below. U= [ a, b, c, d, e, f, g, h, i, j } A = { d, e, g, h,…

A:

Q: 18.1.2. Let R be a commutative ring with identity, and let a, b E R. Assume ab is a unit in R. Do a…

A: To show this, let's consider a counterexample. Let R be the ring of integers Z, and let a = 2 and b…

Q: 3. Prove or disprove: (a) a bc = a | b (b) a | bc and gcd(a, c) = 1 =→ a |b (Hint: recall Bezout's…

A: We have to check whether given statements prove or disprove.

Q: 4. How many sets does the algebra A=(0, X, A, B,C,.....) contain? (This is the smallest algebra…

A: Given that smallest algebra containing { A, B, C }.  We have to find how many sets does the algebra…

Q: Q. 3. A transformation T:R² →R² first reflects vectors through the y axis, and then rotates vectors…

A: Answer 3: We are given a transformation T: R2→R2 that first reflects vectors through y-axis and then…

Q: Q.Let X = {m, n, p, q}, and E= {6, X, {m}, {n}, {p, q}, {m,n}, {n,p, q}, {m, p, q}}. Then %3D > is a…

A:

Q: 4. How many sets does the algebra A=(0,X, A, B,C,.....) contain? (This is the smallest algebra…

A:

Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is_ A. a -2…

A: Given ;a*b=a+b-1

Q: Q2. (a) Prove that if ), and >. are segma algebras over X, then 2n2, is a sigma algebra over X. (b)…

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Q: Q. If >, and E, are segma algebras over X, 12 Eu, is a sigma algebra over X а. '2 b. ,n, is a sigma…

A: Correct answer is option B Explanation is given below

Q: If x and Yare i.i.do ( [0,1] fou's, then obtain и B The Dodof⋅ of x-y

A:

Q: Q. If E, and E, a. E,n E, is a sigma algebra over X b. EuE, is a sigma algebra over X E, E, is a…

A:

Q: 2. (a) Prove that if E, and , then >n, is a sigma algebra over X. (b) Is E,UE, are segma algebras…

A:

Q: . Is the power set P(H),

A: Given,   And the powerset of H: . * and *' on are defined by . We have to justify that the…

Q: Let X = {1,2, 3, 4, 5, 6}, A = {0, X, {1,2, 3}, {3,4}, ...} is a o-algebra on X. Which of the…

A: Given set is X={1,2,3,4,5,6}

Q: From the picture can you prove that is the λσ is one to one and onto? plz with details

A: We have n≥2, and that σ∈Sn is a fixed transposition. Also, we know that the set An of even…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.