2.4.6. Show by example that it is possible for the union of infinitely many closed sets to be open, closed, or neither open nor closed.

Q: s at least one real eger with an even : n of any two even

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Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: 4. Give an example of a non-measurable subset of R. (witheutProof)

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Q: Let d be the highest degree of any vertex in a tree T, and let l be the number of leaves of T. What…

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Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Suppose X is a set with 84 elements that is partitioned into four subsets: X1, X2, X3, and X4. If X1…

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Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its (b) a set…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the set T = {..., −34, −17, 0, 17, 34, ... } with the usual definition of less than (a0).…

A: Completeness property of real numbers:  Every non-empty set of real numbers that has an upper bound…

Q: What is the largest value of r for which N(2.2, r) is a subset of S = ( – 5, 3) U (1.7, 4.6) .

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Q: What is the class width (i) if one of the class interval is 18-26?

A: If class interval given is 18-26 The class width is difference between upper interval and lower…

Q: Suppose A and B are both countably infinite sets. Show that the union of A and B is also countably…

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Q: 5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre- spondences…

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Q: 4) State the condition for equivalnce for measurable set. being a lebesgue

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

Q: A is a subset of the real numbers, R.

A:

Q: 2.29. Let A = [a1, a2] and B = [b, b] be closed and bounded intervals in R. In each of the following…

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Q: Đ A is a closed set.

A:

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

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Q: rsection of any collection of com

A: This is a real analysis question. Let (X,d) be a complete metric space with X not ∅. Suppose the…

Q: 4. Give example of a non-measurable subset of R. (witheut Proef) an

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Q: Let D be digraph. If id(x) > 0 for all x ∈ V (D), then D contains a circuit.

A: Given:- Let D be digraph. If id(x) > 0 for all x ∈ V (D)

Q: 1. Let F be a forest with 50 vertices and 35 edges. How many trees does have F.

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: 3. Let M and N be nonempty set such that M = N, then |M| = |N|. %3D

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Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. <=>…

Q: 4.4 Find a set of 3 points in S' so that dcos does not satisfy the triangle inequality.

A: Please check step 2 for the solution.!

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

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Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has 150 followers and a follower of Jim follows Jim and 149 others. Let the set S is…

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: 1.39. For each point (m, n) in the digital plane, determine the smallest closed set containing (m,…

A: given:  for an each point  (m, n) in the digital planeTo…

Q: ,- ). Show that there a 3,4

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Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: Answer :

Q: If geRla,b] and if h(w)= gcu) encept %D finite number f points for [a, b],'then and in of prove that…

A: First we have to divide the set into finite subsets of x intervals required.

Q: (3.2) Indicate which of the following sets are compact in X. (a) C = {4,n € N}, X = R (b) C = Qn (0,…

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Q: Goenthe luncaan g(n) yon+1dvefor g(@) = 3 Prowde your ansper beluw

A: We have to find the value of n for function g(n) when g(n)=3.

Q: A study by Forbes indicated that the five most common words appearing in spam emails are shipping!,…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: 7. Show that the Obenchain class LOb(B) is a convex set.

A: Given: To show the Obenchain class LOb (β) is a convex set is given as,

Q: Prove S^2 is simply connected.

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Q: w that the set S = 3 6. 4 5 ms all of R³ or find an element of R³ not belonging to span(S).

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: 5. (a) How many functions are there from a set with n elements to a set with m elements?

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Q: 2. Let S be the set [9]: (1.2.9). (c) List 5 derangements of S having 2 in the 3rd position and 5 in…

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Q: In a bag of 350 chocolate candies, 37 of them are brown. The candy company claims that 13% of its…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: ave a class boundary that is less than zero?  On the probelem I am working, the class goes from 0-5

A: Class boundaries are the values which help in separating the data points in statistics.

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: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…

Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .