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 sigma algebra over X AE, is a sigma algebra over X d. None of these. C. O a

Q: 10 -8 -2 -2 0 2 2 -2 24. Let A = and w = Determine 1 -1 1 0 -2 if w is in Col A. Is w in Nul A? 6

A: Consider , A=10-8-2-2022-21-160110-2  and w=2202 To determine if w is in column of A. In matrix take…

Q: 2 Let o (1 3 5)(2 4) and T (1 5)(2 3) be elements of S. Find o,or,to, and to

A: Note: Here the operation is composition of permutation group S3.

Q: finite gooup Q.let G a e G be 1a1=12. ĭ olther generators and 8.7 find all HE ca> H. of

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Q: .6. Let a, b, c € Z. Use the definition of divisibility to directly prove the following roperties of…

A: Definition of divisibility :

Q: 8. Let = {(0,²) In = {(0,²) n = 1,2,3,...}. Prove that n = 0.

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Q: (1 2 3 4 5 5 1 3 6 2 2. Let o = E S6. 1. Wi des 2. 3. 4. What is the size of the conjugacy class of…

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Q: Let -8 -2 -9 6. 4 8 and w = 1 4 4 -2 Determine if w is in Col A. Is w in Null A?

A: We can solve this using given above information. -8-2-9648404 and W=21­2 First we calculate Col (A)…

Q: b. Let A and B be elements in Sn T. Show that An BE S N T. c. Let A¡ be elements of SnT for i € I.…

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Q: .3 T Evaluate In In e²+j²4

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Q: Which of the following sets are the base for R ? Explain the reason. a) S = {(1,1,0, 1). (1, -1,1,…

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Q: Let f E S, be a permutation What is the value of the signature function sgn(g) for the following…

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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: 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: a. Find C if C = AʘB.

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

Q: 3. For all æ E Z[i], there are N (x) elements in Z[i]z.

A: The set of Gaussian integers is a subset of the set of complex numbers containing the elements with…

Q: 13. If T is self-adjoint, then S*TS is self adjoint for all S; if S is invertible and S*TS is…

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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: Prove that if n 2 3, the only element o of S, satisfying oy =ya for all y E S, is the identity…

A: Let n≥3. Let σ∈Sn such that σγ=γσ for all γ∈Sn. Suppose σ≠i, the identity Then there exists…

Q: Following is a Discrete Structure question.

A: We need to prove the following.

Q: Consider the following permutations in S9 1 2 3 4 5 6 7 8 9 (1 2 3 4 56 7 8 and r= 3. 5214 6. 9 78 5…

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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: 3. Let n e Z be nonzero and even. Prove that there exist unique a € {0, 1}, b € N, and odd c€ N such…

A: Since n is even and non-zero . Since n is non zero ⇒ n is either positive or negative. Let's write…

Q: 4. Write a wff of P that is equivalent to the following wff involving a different quantifier.…

A: Given:                              ∀zNz∧Wz To do: Write a well formed formula wff equivalent to the…

Q: 6. Prove that if gcd(a, b) 1, then gcd(a +b, ab) = 1. %3D %3D

A: Given that gcd(a,b)=1 If possible , let us assume that  gcd(a+b,ab)=d,d≠1 Then the number d must…

Q: What are the elements of (AUB)?

A: SOLUTION-

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: 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: 7. With I as in Exercise 3, write out the distinct elements of E/I. XX 1 T

A: this is to help you further with your question. and provide appropriate answer for it. thanks

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: J. nA(D) < // f(x, y) dA < M A(D) D is estimate to find an upper bound f (2 – y)/4 ITX 4 (쓸) dx dy.…

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Q: Q. 7. Is the power set P(H), which is the set of all subset of H 1,2 with the operations of and a…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.