Given the following sets X= {a,b,c} Y= {a} Z= {a,d} In the universe U= {a,b,c,d,e}, what is (X’ intersect Y) U Z?

Q: Let A be a set. Prove that S = 0. SEP(A)

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

A: Given u=4-1 , v=41 and b=xy. The vector b=xy is in span u,v if the system containing u,v and b is…

Q: Complete the proof: If A≤B and B≤C, then ACCn(transitive property for set in inclusion) Need to…

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Q: 1. For a subset YC (X,T ) , show that the collection TY ={Y NUJU ET} is closed under finite…

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Q: If S is compact and D is in S is a closed set, then D is compact. Use the definition of…

A: Let S is compact and D be a closed subset of S. We are to prove that the set D is compact in S. Now…

Q: Given that U = {1,2, 3, ..., 11, 12, 13} A = {1, 2, 7, 12} В 3 3,5, 6, 8, 12, 13} С 3 {1,5, 7, 8,…

A: Explanation: Region I:   2 Region II:  Null Region III:  3,6 Region IV:  1,7 Region V:  12 Region…

Q: For the set A= [-0, 4) U{5,9} U[6,7] , 6 is interior point of A ylgn İhi

A: False

Q: (a) Consider the following topology of X = {a,b, c, d, e}: T = {X, 0, {a}, {c, d}, {a, c, d}, {b, c,…

A: In topology and related branches of mathematics, a connected space is a topological space that…

Q: O Show that if Si and S2 are convex sets in R™X", then so is t mxn S = {(x, y1 + y2) | x € R", y1,…

A: Convex set: , If a and b are points in a vector space S. Then the vector space is called convex set…

Q: Show that the following pairs of sets S and T are equinumerous by finding a specific bijection…

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Q: Let d and e be metrics on a set X such that for each ball Ba center at pE X there exists a ball Be…

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Q: of all Z € C that z iz e = e a Descnibe and sketch the set

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Q: Show that if S x T is a closed subset of R2, then S and T are closed subsets of R.

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Q: (a) For the following subsets in an indicated metrie space detennine the interior, boundary points…

A: See the attachment.

Q: 1. Prove that for all sets X, Y , if XU Y = Xn Y, then X = Y. %3D

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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: be any nonempty set and let µ* be an outer measure on P(X) and let A, B e P(X). If at ne of A, B is…

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Q: Sketch the following sets and find which sets are open, closed, domain and region |z – 1| = |z – i|…

A: Note:- you have asked multiple independent question. we will answer first three questions for you as…

Q: Q: In usual topological space (R.Tu). answer the following: 1- Is [0,1] is compact set in R? Why?…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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Q: Consider the following subsets of R equipped with the Euclidean topology: A = { neN} Зп — 1 n+1 ° B…

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Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

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Q: Suppose that X, Y subset U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr(X intersect Y)= 0.09, what is Pr(X’…

A: Given, Pr(X)= 0.35 Pr(Y)= 0.36 Pr(X intersect Y)= 0.09  Pr(X’ U Y)=?

Q: Let the non-empty set S {x-y3:x,y E R}, show that S is closed'under multiplication then find the…

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Q: Suppose S and T are balls with the same center. Show that one of them must be a subset of the other.

A: It is given that S and T are balls with same center. Let the center of the balls be a. Assume that…

Q: Let (X, M, u) be a measure space wE

A: Given, (X, Μ, μ) be a measure space where μ is a probability measure. Assume thatf, g : X→ℝ are…

Q: Prove that in any metric space (S, d) every closed ball S,[xo] is a closed set.

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Q: With help of Venn diagrams show that the following are indeed true: a.X n (Y U Z) = (X n Y) U (X…

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Q: Let X be a set with more than one element. (X,t) is a topological space such tha Vxe X,{x} €T then…

A: Given a set X with more than one element.

Q: 5-The Center of aringR dented by cent CR)is the set Cent CR) - [CERIC.X = X-C,V XER? %3D Prove that…

A: solution You just need to prove that the centre is a ring within itself. Associativity of both…

Q: Let X be a set with more than one element. (X,7) is a topological space such that Vxe X, {x} €T then…

A: Given the set X contains more than one element.

Q: 4. Let (X, d) be a metric space, r E X, e > 0, and E = {y E X : d(x, y) < e}. Show that E is closed.

A: Let (X,d) be a metric space, with x∈X , ε&gt;0, and E={y∈X:d(x,y)≤ε} To show: E is closed. That is…

Q: Indicate whether the following statement is true or false? 1. If S = span{u1, u2, uz}, then dim(S) =…

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Q: Set C and the universal set U are defined as follows. U={p,q,r,x,y,z} C={p,q,x}

A: Given,        Set C and the iniversal set U are defined as follows :         U=p,q,r,x,y,z…

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: 7 The set M={xEN:x<÷} with the usual metric is connected.

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Q: consider R with the usual topology then a subset A={1,0.5,..} is: empty or closed or open or none…

A: Given R with the usual topology and given a subset  A=1, 12, 13,.....

Q: hade in the region(s) that represent the set (AU B)nC' В A

A: Solution of the problem as follows

Q: let A Set bounded below, ילC erove that C. nf A inf C A %3D

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Q: (iii) If (X,r) is topological space, A,BCX. Prove that (a) b(A)=AA (b) If ACB, then d(A) ≤d(B)

A: First part Is obvious from definition of boundary points of a set.

Q: I. Find the Lebesgue measure of each of the following sets and explain why: 1. m(-0.1,1.5)) 2. т (R)…

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Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your U A •y…

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Q: Given the set T := {(x, y) ∈ R^2 : |xy| Less or equ 1}. Is T a compact set? Show your working. If…

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Q: Let the non-empty set S = {x - yv3:x,y ER}, show that S is closed'under multiplication then find the…

A: We have to show that the given set S=x-y3:x,y∈R is closed under multiplication and also find the…

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…

Q: let E be a set that baunded. Prove that Inf E = Sup -E) where R, XE E y

A: To prove for a buonded set E inf(E) = -sup(-E) , where -E = {-x, x belongs to E} , we first prove…

Q: Let N be with the discrete topology If A=(1,3,5..), then Bd(A)=

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Q: Let X= (3, 5] u {6,7,...} and A= {5,6,7} and metric defined on X as d(x,y) = |x - y|

A: Note: As per bartleby instruction when more then three questions for subpart is given only three…

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.