QU({-1,0,9,11,17} x {-n, n}) is an empty set O an uncountable set O a countable set Let A = {x E Z: 10lx} and let B {x€Z:15lx}. Then A=B

Q: (1) Let X be an infinite set and set r to be the set given by T = {0} U {U C X : U° finite}. (a)…

A: τ={ϕ}∪{U⊂X :Uc is finite }  (a) Xc=ϕ, which is finite . so X∈τ let A,B∈τ Then Ac,Bcare finite…

Q: The set of all ordered triples of real numbers with the operations (x, y, z) O (x', y', y') = (x +…

A:

Q: Let R be the set of all real numbers with the euclidean topology. Show that R has an uncountable…

A: We will first show : (iii) If S is dense in X, then T is dense in X, where S and T are non-empty…

Q: Suppose Y=[ 0 ,2 ) . In this case A=[1,2 ) is not closed in X; while closed in Y. In addition, G=[0…

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Q: Q3- Give an example of two denes not equal X subsets of (R,7) and (z,7cof). ( Explain your answer ).…

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Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x EX and y EY and (y * -…

A: This is a problem of set theory, and R is a subset of X×Y

Q: Prove and show complete solution: Let ƒ be defined on an open interval (a, b) and assume that for…

A: please comment if you need any clarfification. If you find my answer useful put thumbs up. Thank…

Q: التاريخ 27 أمر موح let I = (a,b) be an open interval show that - for every positive sM(IDS.

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Q: Let X = {a, b, 1, 2, 3} and T = {X, p, {a}, {1,2}, {a,1,2}}. Let B = {b,3} * B is dense in (X,T) B…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Sets L and Jare defined as follows. L = {g,h, i, j, k} J = {i,l, m, n, o} || || Find the…

A: Given, sets L and J are defined as follows: L = {g,h,i,j,k} J = { i,l,m,n,o}

Q: Show Corollary 1.24. Namely, show that a measure space (X, M , μ) is complete if (X, M , μ) is…

A: Let X be a measure space with σ-algebra M and the outer measure μ. To prove that X is complete. That…

Q: Let U = (0, 1) U (2, 3) U (4, 5) be a union of three open [0, 10] \ U. Show that A is compact. 2.…

A: Que  Ans : given         U = (0,1)U (2,3) U (4,5)  be unian              of 3 open sets    A= [0,10]…

Q: Prove the theoreom : The set Z is denumerable.   solve it fast plz discrete math

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Q: Which of the following subsets of R² are open? From the 5 choices, select all that apply {(x, y) : y…

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Q: Which interval notation describes the set S= {x | 1s x < 10}? 1. [1,10] 2. (1,10] 3. [1,10) 4.…

A:

Q: Let U ⊆ ℝ be an open set. Then U is the union of a countable, disjoint collection of open intervals.…

A: Given: U=∪i∈Iai, bi where I is a countable set, ai, bi∈ℝ, ai=−∞, or bi=∞ for all i∈I. To show: ax∉U

Q: Prove the following parts of Theorem 2.2.1: For all sets A , B and C A ∩ A = A

A: For A ∩ A =A, A ∩ A⊆A and A⊆A ∩ A

Q: tor all l sets A, Bad C やok that A xCB-c) = (AX1B J- CAxc). %3D

A: Given below the detailed solution

Q: (3) X is not the union of two disjoint non-empty separated sets. (4) X is not the union of two…

A: as given all the conditions are equivalent  (4) To show - X is not the union of two disjoint non…

Q: Let U = (-0, ), A = [-1,6], B = [-6, 2). In interval notation, determine An B. Let U = (-00, 00), A…

A: Brief explanation of the answer has been provided below.

Q: dafine Let A and B n@t be the cardinality f a set 3. It n CA-B) = 18, n CAUB) = 70 nCAnB)= 25, be…

A:

Q: N Hid 4. Let T consist of 0, R, and all intervals of the form (-0, p) for p E R. Prove that T is a…

A: You can do this only when maximum always exist but it is not necessary that it always exist because…

Q: A and the set B = {x, y}, then A X B is denumerable as well.

A:

Q: 8. Let U = (-00, ), A = [-1,6], B = [-6, 2). In interval notation, determine An B. 9. Let U = (-0,…

A:

Q: Least upper bound (lub) ond gueatest lowr bound 1.b) af the set are.

A: Just explore the set and look for biggest and smallest elements of given set.

Q: Q. Determine whether the given set V is closed under the operations addition and multiplication…

A:

Q: Let a, m be real numbers. Applying Triangle inequality (m, 0,1,2) and to u = = (a,-1,-1,0), we get

A: Given that       u = (m,0,1,2) and v = (a,-1,-1,0)

Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

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Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

A:

Q: Vhat does "x is an upper bound of a set S C R" mean ? State the Smallest Upper Found Principle.

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Q: Let A and B be finite sets satisfying |A| = 7,|B| = 8 and |An B| = 3. %3D Calculate the following:…

A:

Q: Let S = {-3,-1,0, , 1, v3, 3, 9}. Which subset of 1 S contains the elements that satisfy the…

A: Given- S=-3,-1,0,13,1,3,3,9 To Find- The subset of S that contains the elements that satisfy the…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, [n-1, 12n+1]}, be a family of elements…

A:

Q: I) We know that -5,-4,-3,-2,-1 and IN are well-ordered sets with respect to the trivial ordering.…

A:

Q: 3) Let D = {(x, y) E R² | 0 < x² + y² < 4}. Give all boundary points of D. Is D open, closed or…

A:

Q: nts] "Prove" (using graphs if necessary) whether the set {(x, y): x = 0 or y=0} < R² is: a closed…

A:

Q: Express the set W = {x| -6 < x < 1} using interval notation. %3D Box 1: Enter your answer using…

A: The set is given by: W=x|-6&lt;x≤1 This means that -6 is excluded and 1 is included in the set. It…

Q: Exi meaning collecting of x set

A: The objective is to state whether the given statement is true.

Q: Set of Space. d f Real number R is veeter An d is Spale

A: We know that ℝ,+ is an abelian group. Now define scalar multiplication on ℝ by α.a=αa where…

Q: Let A andB be two sets of. integers. A distance measure 'd is defined as d(A - B) = size(A - B),…

A:

Q: I) We know that F-5,-4,-3,-2,-14 and N aire well-ordered sets with respect to the trivial ordering.…

A: Step:-1 Well ordering Principle:- An ordered set is said to be well ordered if each and every…

Q: 25

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Q: (iii) The outer measure is translation invariant i.e. for every set A and for each x = R, m* (A + x)…

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Q: Express the set W = {x | x² < 4} using interval notation. %3D Box 1: Enter your answer using…

A: The set of points is defined by the following inequality is  W =  x| x2 ≤4  To evaluate : The set of…

Q: Let R (the set of real numbers) be equipped with the Euclidean topology and let S = {0, 1, 1/2, 1/3,…

A: We will check each options

Q: 1.(a) Let B = (i, i+ 1], open closed interval, where i EZ the integer. Find U, Bi, (b) Let An = {x:…

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Q: (Q x {-n, n})U{-1,0,9,11,17} is an empty set a countable set an uncountable set

A:

Q: Specify the boundary and interior of the set S in 3-Space whose points (x,y,z) satisfy the given…

A: Given : S = (x, y, z)∈ℝ3 : x≥0, y&gt;0, z&lt;2 To find : (I) The boundary and interior of S,  that…

Q: 1- Let X be a non-empty set and r ((-o, a)| a E R) URU (4) then r is called: (11) Indiscrete (1)…

A: Let (X,T) be a topological space. Let A⊂X be a subset. Then intA is the largest open subset of A.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.