5. Let r € R and A, = {q € Q : q < x} . Prove sup A, = x.

Q: - 21 , Prove that + (n? m' ) yn=o 2.

A: According to the Leibnitz theorem, dndxn(uv)=C0nunv0+C1nun-1v1+C2nun-2v2+... Formulae used:…

Q: Prove that (C, +) ≈ (R × R, +).

A:

Q: The value(s) of x that satisfy In(x² + 1) – 2 In(x) = In(16) – In(8) are/is

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Q: 2. Let S be a bounded set in R and. let a < 0. and let aS := {as : s E S). Prove that inf(as) = a…

A: Let S be a bounded set in R and let a&lt;0. And let aS := {as : s belongs to S}. We have to prove…

Q: Prove that the set S = {n² : n e N} is denumerable. %3D

A: We have to show that the given set S is a denumerable set.

Q: Show that if A is closed in Y and Y is closed in X, then A is closed in X.

A:

Q: 6. Prove that if alb and k E Z, then a|(b+ ak).

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Q: 21 - Let V = R3,S = 5 Show that = Span(S) %3D

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Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: Find a set of 3 points in S' so that dcos does not satisfy the triangle inequality.

A: The sine distance between two points x,y∈ℝ2 is defined as: dsinx,y=x.yxy and the cosine distance…

Q: If S, T are nonempty bounded subsets of R with S ⊆ T, then inf T ≤ inf S ≤ sup S ≤ sup T.

A: Since S ⊆ T it follows taht inf T ≤ t, ∀ t ∈ T, then  inf T ≤s , ∀ s ∈S:Therefore inf T is  a lower…

Q: Show that a set {V1, ..., Vp} in R" is affinely dependent when p > n + 2.

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Q: .1כ If n33, еxpand u %3D а'хх, a" x,x;

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Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

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Q: 11. Let SC R and suppose that s := sup S belongs to S. If u ¢ S, show that sup(SU {u}) = supfs*, 4).

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Q: Let A,BE Mmna Shaw that vTAw= V' Bw for all VER™ end WEIR" if and only if LA=B. %3D

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Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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Q: Let S andl T be twa mat &ices for thera Xespective epaption Ome! and T theis despachive Canjugate..…

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Q: In AAGE and AOLD, ZGAE = ZLOD, and AE OD. To prove that AAGE and AOLD are congruent by SAS, what…

A: Given Data: Congruent angles:∠GAE≅∠LOD Congruent sides: AE≅OD The triangles △AGE and △OLD are…

Q: Consider o Con Assume He holding holding Vo =Vi =d, thatis, to the ofter going 1. Draw the Pre

A: Hi, there! As per the norms, we are allowed to solve single question at a time when multiple…

Q: Prove that (S ⋂ T)c = Sc ⋃ Tc and  (S  ⋃ T)c = Sc ⋂ Tc .

A:

Q: snip

A: Inner product of two vectors is equal to sum of product of corresponding elements of the two…

Q: Let A be a 7*4 matrie. What must a and b in or der to TO= Ax?

A: For it to be possible that two matrices A,B  can be multiplied as AB then we must have number of…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are…

A: Solution ::

Q: Let x, y, A, u E Z. Prove that if 1 = Ax + µy then r, y are relatively prime.

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Q: If tanh '() = 1- 12/3, then z = %3D In + 종 In O In In

A: As per the question we have to solve the complex equation and find the exact value of the complex…

Q: Let SCR. If sup S (resp., inf S) exists, then it is unique. ylgn ihi

A: The supremum (or least upper bound) of a set S ⊆ R which is bounded above is an upper bound b ∈ R of…

Q: 2) Let a,bE Q such that a<6. Prove that ax <bx.

A: The statements can be proved by analyzing the results from the given statements. The other methods…

Q: 1. Create a paragraph proof. Given: ZWVX = LYXV ZYVX ZWXV Prove: AVXY = AXVW V

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Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: Show that S={(1,0,1), (1,1,0), (1,1,1)} is liearly independent. Give a proof.

A: Vectors in a set are linearly independent if the matrix formed by the vectors as the columns of the…

Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: 3. Suppose (a,n) is Cauchy and that for all m, k 2 100, Jam - as 0. Does it follow that the…

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Q: Apply any method to prove that a|b (or a nand b), which is defined to be ¬(a ^ b) is complete. Write…

A: The NAND &amp; NOR gates are called universal gates as they perform all the logical operations of…

Q: (4) Let A CRbe a et ith greatet element a E A Prove that sup(A)=a

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

Q: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

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Q: Prove the following using resolution refutation: 4. Given: (p Aq) -→r, p^ s A~w, (s A t) →q, tv w…

A: Given 4 premises p∧q→r, p∧s∧~w, s∧t→q, t∨w. The conclusion to be proved is r. We know that a…

Q: Let X, , X>, . X, be a vandam of size I For o hormol distribuien with unrur M and $6. IS 5 Xi = 132…

A: Provided information is ;  sample size(n) = 11 ∑i=1nxi  = 132 ∑i=1n(xi-x¯)2 =99 confidence interval…

Q: 12.42. Let a, be Z, where not both a and b are 0. Prove that if d = gcd(a, b), a = ajd and b = b1d,…

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Q: Given: STaVU T. Prove: 4SVTZUTV

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Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

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Q: a nonempty compact set of IR. sup Ke K. be

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Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: Suppose that r, s are integers (possibly different from x, y res that ar + bs = c. Show that there…

A: Introduction: Let us suppose that two integers are a and b, greatest common divisor of these two…

Q: 2/ Let fcantinous appicatiom Prove thet Fles sf)/BE then SePose fcef) and Proye fis continates a ff…

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Q: Prove that S UT = SN T for all sets S and T using the rules for complements of sets.

A: rules of complements x∈A⇔x∉A¯

Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.