For each matrice A, show for definition norm A we can write: |A| + -1

Q: For any sets A, and B we can write an algebraic proof to prove that A– (ANB) = OB {} A - B Bc

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Q: Let T be the Euclidean topology. Let A = [0,2] and B = [0,1[, then B is clopen in (A, TA) where TA…

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Q: b) BCA iff A n B = ¢ c) (A – B) U B = A iff B C A

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Q: * Let R be with the indiscrete topology. If A = {1,3, 5, 7, . }, then A' = A O N O RO

A: This question is related to topology, we will use the definition of indiscrete topology to solve it.

Q: In Question,determine whether the definition gives a norm.

A: p(x)=p(0)+p(1)-p(0) for p(x) in P1

Q: True or false? For all sets A and B,  (A∪B)'=A'∪B' This can be determined by constructing a…

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Q: 3. Let A, B be nonempty sets and a,b ¢ A, 1,2 ¢ B. Show that if A B, then AU{a, b} ~ BU{1,2}.

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Q: If a < b, then [a,b] CR does not have con- tent 0. In fact, if U1,. . .,Un) is a finite cover of…

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Q: C) = (*,') + "- ), Give an interpretation involving subsets. Problem 4) Prove that

A: See the hand written

Q: Which of the following set S is a spans R"? a. S = {(2, 1), (2, 1)} b. S = {(1,2, 3), (3, 2, 1)} c.…

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Q: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =B

Q: Let A = {a,{a}}, B = {0,b}, C = {{0}.c.{o.c}}, D = {0}, and E = {e}. Find: a) Cx D= b) B2= c) P(B)=…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Fix n ≥ 1 and let A be a non-empty closed subset of Rn such that if x, y ∈ A then (x+y)/2∈ A. Show…

A: The given details: Fix and let A be a non-empty closed subset of Rn such that, Show that A is path…

Q: Use the tabular method to to prove the following in general: 1. (An B) C (AU B) 2. The O is a subset…

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Q: For any sets A, B, and C, prove that Ac Bnc if and only if A c B and A CC

A: Consider the statement,

Q: Show that the set (1) isopen u k = 1 and find its measure.

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Q: ℘(A) ∪ ℘(B) ⊆ ℘(A ∪ B). Is ℘(A) ∪ ℘(B) = ℘(A ∪ B)? Either provide a proof to show that this is true…

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Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(2, 1,−2)T, (−2,−1,…

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Q: Find the glb and hub of the following sets. Which of these belongs to the set. (a) A = (b) B=…

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Q: If vo and V, are respectively the t-conorms that are dual to the t-norms Ao and A5 respectively.…

A: In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary…

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

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Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

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Q: Q2: Let the set under consideration be N for each n EN, define u, = {n, n+1, n+2, ...} and let 1 =…

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Q: 5. If {T,} is a family of topologies on X, show that Ta is a topology on X. Is UT, a topology on X?…

A: First we will prove the result that arbitrary intersection of a topologies is a topology by showing…

Q: Let D be an n-vertex digraph with no cycles. Prove that V (D) can be ordered as v1, . . . , vn such…

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Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: Let A, B and C be sets. It is given that AUC= BUC and AnC= BnC. Shơw that A = B.

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Q: Let A is the set of vowels in the word "TRIGONOMETRY". Write all subsets of A.

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Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

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Q: Which of the following is true for any set A?

A: HERE FOR TRUE SENTENCE FOR ANY SET A . EMPTY SET IS  SUBSET OF ANY SET

Q: Prove: If U is a neighborhood of x0 and U ⊂ V, then V is a neighborhood of x0. Also, if U1 ..., Un…

A: The neighborhood of a point: Let (X, T) be a topological space and x0∈X. A neighborhood of x0 at is…

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Q. Let (X, B(R), µ) be a Borel measure space. If An BnC ¢,determine µ(AUBUC).

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Q: If T is surjective and V = span(3), prove that W = span(T(3)). Hint: given that span(T(3)) ≤ W, it…

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Q: Determine whether the following define norms onC[a, b]:||f|| = |f (a)| + |f (b)|

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Q: Consider the following subset S C R 1 -3 S = -2 -10 8 Is span(S) = R*? Explain your reasoning and…

A: See the attachment

Q: 3) let X be discrete topology and Ac X, find A ?

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Q: Let A,B, be Subeet R. state the conditiuns which make the pair (A,B)a Dedekind cut

A: Consider the given information.

Q: 2. Let a Find the Span(a)

A: Given: a=00 To find: Span(a)

Q: 3. Show that if A and B sets then A – B = ANB (Note that: Using Venn Diagram is not accepted!)

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Q: Let be 7= {x, 0, {a}, {cd}, {a,c,d}; {b, c, d, e}} topology on X = {9₁b, c, d, e}. Check if X is…

A: A set X is connected if and only if X can not be written as union of disjoint open sets. An element…

Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r…

A: The given set is S=1,1,1,2,2,1,3,2,3,3. We know that the polytope:…

Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

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Q: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: Call an L-tile to be the following shape Prove that for any nzl, a 2" With a 1 x 1 Corner Sauare…

A: For n = 1 each of the four 2×2 checkerboards with one square removed can be tiled using one right…

Q: Let Cc R be a connected set and a , be R. Prove that [a , b] c C.

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Q: Exercise 3.6 Prove that if (X, A, µ) is a measure space, B e A, and we define v(A) = µ(AN B) for A E…

A: Given X,A,μ is a measure space and B∈A.  Let X  be a set and A be a σ-algebra on it. A measure ν is…

Q: Let T = {X. Ø, {b}, {a, b}} be a topology on X = {a,b,c} and let A = {a,b,c}, B = {a,b,c}. Find a)…

A: Given That: Let T={X,ϕ,{b},{a,b}} be a Topology on X={a,b,c} A={a,b,c} ,B={a,b,c} To Find: a)…

Q: (b) Let (X, >, ) be a measure space. For A, Be ). Show that μ(AU B ) - μ(Α) + μ(Β) -μ(An ). %3D

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