Q2. (a) Prove that if , and E, are segma algebras over X, then . Σ is a sigma algebra over X. (b) Is UE, a sigma algebra over X? Prove your answer.

Q: R Let ) be a o- Algebra on X. Assume that y, u :2→ [0, 0) are two measures onX.Then - 3y + 2µ is not…

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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: Q3. (a) Let X = {m, n, P, q}, and = {0, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}. Is > a…

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Q: Prove that Zn has an even number of generators if n > 2. What doesthis tell you about Φ(n)?

A: To Do: We have to prove that Zn has an even number of generators if n>2. Also, discuss what does…

Q: • Determine the elements of [i]/(1+2i). Note: (1 + 2i) is Į [i] is a Hint: It has an I deal .…

A: Determine the elements of ℤi1+2i Note: 1+2i is an ideal and ℤi is a Gaussian ring. Hint: It has 5…

Q: Σ1 (3)* (?)² i=1 ►Give a combinatorial proof of the following identity (3η) = (²n) HINT: Remember…

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Q: 2. Find the characteristic of the following rings. (RS is defined in Exercise 47 of Section 5.1.) a.…

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Q: Exercise 3.9 Suppose X is the set of real numbers, B is the Borel 0-algebra, and m and n are two…

A: Given X=ℝ, the set of all real numbers. The a Borel σ-algebra, B,  is a  σ-algebra generated by…

Q: R. K Which of the following is sufficient to prove that A IJK is similar to A RST? A. ZI ZR and ZK…

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Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: Q. If E, and , are segma algebras over X, 2uL, is a sigma algebra over X b. ,nE, is a sigma algebra…

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Q: 7. Consider the identity: k n n = n a. Is this true? Try it for a few values of n and k. b. Use the…

A: hence proved.Explanation:Step 1:Step 2:

Q: (i) If A E F and BE F then ANBE F. (ii) If A and B are subsets of N such that ANBE F then either A E…

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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…

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: (a) Let X = {m, n, p, q}, and = {ø, X, {m}, {n}, {p, q}, {m, n}, {n, p, q}, {m,p, q}}. Is a sigma…

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Q: Let =P(N), then & is Boolean algebra. ulgn

A: True Statement

Q: limf, is measurable 00 ylan ihi

A: GIVEN a statement

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: Find the Boolean product AOB where A and B are defined below. [1 0 1 A = 0 1 1 1 1 0l [1 0 1 B = 0 1…

A: Here given that                           A=101011110       and       B=101010100 We have to find…

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…

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Q: Q.Let X = {m, n, p, q}, and E= {0, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}. Then is a…

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Q: Let S = R−{−1}. Define an operation ∗ on S by a∗b = a+b+ab, a,b ∈ S. (6.1) Show that S is closed…

A: (6.1) Let, a, b ∈ S.      Then, a and b are real numbers such that a ≠ -1 and b ≠ -1.      Now, a ∗…

Q: Let -{[:);}--{:)[:} -{{)}} Both B and C are bases for R2. If {x}s =: -[:], what is {x}c?

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

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Q: Q3. (a) Let X = {m,n, p,9}, and = {ó, X, {m}, {n}, {p.q}, {m, n}, {n,p, q}, {m, p, q}}. Is a sigma…

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Q: Write an equation for the function graphed below 15+ 14+ 13+ 12+ + + + -7 -6 -5 -4 -3 -2 -1 -1 -2 -3…

A: A following graph:To Find:Equation of the above graph.

Q: n m+n ) (₁ - ₁) + - + ( ) ( ) = (";"). (™+"). r > a. in valid

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Q: 1 a b Let G a, b, cE Z. Prove that G is isomorphic to D4

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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.