What is the characteristic function of set A = {1, 3, 8, 12}? Prove A U (BnC)=(An B) U (An C), given A = {3, 6, 8}, B (4, 6, 9}, and C = {4, 8, 9}.

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: Please check the next steps for detailed answer

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A: From the graph, v(t)=dstdta(t)=dvtdt

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A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Let x = {1,2, 3, 4} and P= { {},{2,3} , {43} - っ- %3D nd

A: X=1,2,3,4P=1,2,3,4

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Q: Prove the following version of Darboux's Th

A: To prove the Darboux's theorem:

Q: . Prove that an→L = Jan] → |L]. (Make cas

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Q: 1) If the rational preferences of a consumer over bundles of (x₁, x₂) satisfies which of the bundles…

A: Solution of the problem as follows

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Q: Prove H'n(x) = 2nHn−1(x), n = 0, 1, . . .

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Q: Prove that MSE(Ô) :

A: Consider, MSEθ^=Eθ^-θ2 Here, θ is parameter and θ^ is an estimator              =Eθ^-Eθ^+Eθ^-θ2 add…

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: Prove %3D 11

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A: Given that X,A is a measurable space. The objective is to prove that the sets  {x∈X:f(x)<g(x)},…

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: B) Show that coth-x = In ()

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Q: Show the the Sar induce

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Q: Compute ø(25) for the homomorphism ø:Z→S, such that p(1)= (1,4,2,6)(2,5,7) (1,6)(4,7) O None of them…

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Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

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Q: . Let X;, i = 1,2, · . be a sequence of random variables defined on (N, F). Let (N, G) be the…

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Q: 2. Using exclusively induction, prove that, if X, X1, X2,..., X, are sets, then Xn(X, UX2 U..U Xn) =…

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Q: az Find if yz – In z = x + y ax

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Q: If E, and E2 are measurable , then (E,UE,) is not measurable . صواب İhi

A: Here we have given E1 and E2 are measurable sets

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A: The kernel trick provides a solution to this problem. The “trick” is that kernel methods represent…

Q: 13. If t={X,Ø,{2,4},{1,4},{1,2,4},{4}} is a topology on X={1,2,3,4}, let A={1,3,4}, then Int(A)= *…

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Q: 5. Verify that if U is open in X and A is closed in X, then U-A is open in X, and A- U is closed in…

A: We have given that , U is open in X. A is closed in X. We need to show that , U - A open in X. Also…

Q: Queshon 6) Compute the arthogonal projection of 8 onto the Line L through -S] and the origin. -6 LS.

A: We have to find the orthogonal projection of v on the line through P and the origin.

Q: Let (X, F) be a о — algebra o - , and be two probability measures on (X, F) so that both are ergodic…

A: Let (X,ℱ) be a σ-algebra and μ≠v be a two probability measure on (X,ℱ) So that both are ergodic for…

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A:

Q: Suppose that {Ai}iel and {B;}jej are families of nonempty classes with the same index class I. Prove…

A: Please check the detailed answer in next step

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Q: Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use…

A: Cauchy-Swartz Lemma : For any real numbers  and  the following inequality holds  ,

Q: Prove: le* a. ſ csch x = In - |+c lex+1

A: As per Bartleby guidelines rule I am answering only first question as Both question is not subpart…

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Q: Let fELoi Show that i for any E>o, the set 3- S has a positive measure -

A: For f∈L∞ , f∞=infM>0:μx:fx>M=0For M>0, defining the set AfM=X:1 fx>M⇒For f∈L∞,…

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A: Given, We want to prove that

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A: It is given that,  If g is continuous and ∫-28g(x)dx=30 We have to find ∫-144g(2x)dx=?

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A: Note: Since you are asking the prove for Newton's forward interpolation, but the given formula is…

Q: If E and E, are measurable , then (E,UE) is not measurable

A: False.

Q: Consider f : X →Y, with domain X = {c,j,v, m, e, s, n, q, u, d, i, g} and codomain Y = {80,08, 57,…

A: SOLUTION-

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A: Given :  To determine the polynomial fx of degree 3 that has the following zeros : -8, 3, 0

Q: 2. Prove that [0,1] and U-1 An , where A,= [2n, 2n+1] have the same cardinality. %3D

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Q: 4. Find the number of surjections from {1, 2, ..., m} to {1, 2, .. ., n} such that no element in the…

A: We have to find the number of Surjection from one set to another set.