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

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

A: (b). We consider the example of a set which is not a nbd. of any of its points.

Q: Construct the intersection graph of the following collection of sets: 4 = {0,+2, 14, 16, ±,..} A, =…

A:

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

A:

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…

A:

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: bag of 330 chocolate​ candies, 34 of them are brown. The candy company claims that ​13% of its plain…

A: Formula : Significantly low value = u - 2 * σ

Q: Let (X, E, µ) be a measure space. Justify through an example that the hypothesis µ(X) < o in…

A:

Q: If E <R, then for any 0 <E or an open set there exists b such that m * (G – E) < ɛ. Give an example…

A: For any non measurable set E, the above relation does not hold. The Example of such non measurable…

Q: . Let 7 = {rn}~ be a sequence of real numbers. Prove that the limitpoint set of T is a closed set.

A: Given that x¯ = xnn=1∞ is a sequence of real numbers . We have to prove that the limit point set of…

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: => find fundamental set of Se yo=-3x²e-3x ZR 7:

A: We have to find the fundamental set of solution.

Q: Determine whether is a linearly independent set of vec- 3 11 tors in R3.

A: A set of vectors v1,v2,v3,…,vk in a vector space is said to be linearly independent if…

Q: 5. Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

A: To show that the least upper bound of a set of negative numbers cannot be positive.

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

A:

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: Suppose metric space X is not path-wise connected then X is not connected. O True O False

A: Question 9 Answer: as a path connected space of employees connected but converse is not true. So I…

Q: If S and T are nonempty bounded subsets of the real numbers, show that if ScT Then infT < inf S <…

A: Given ,  S is subset of T

Q: be an open subset in C and f

A:

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

A: (b) Given the example of a set which is not a nbd. of any of its points

Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: 3. What are the restrictions on x?

A: It is known that side length cannot be negative. This implies that, 3x+2&gt;03x&gt;-2x&gt;-23 First…

Q: 6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤…

A: Please find the answer in next step

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To prove that the given fuzzy set is convex and to determine the α-cut sets for the given values of…

Q: 2. Show that the set 3 S = 3 2 2 2 2 spans all of R³ or find an element of R' not belonging to…

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Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

A:

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: Show that Let ECR" is measurable set. If µ(E) >0, then E have a non-measurable subset

A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…

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

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

Q: 5. Suppose that A and B are bounded subsets of R. Prove that AUB is bounded and that sup(AUB) =…

A: Given that A and B are bounded subsets of R.   We have to Prove that AUB is bounded and that…

Q: In a bag of 380 chocolate candies, 40 of them are brown. The candy company claims that 13% of its…

A:

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: To choose correct option from given question.

Q: (ii) Find a connected subset of R² which is not convex.

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

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

A:

Q: 5. Show that the following sequences of sets, {Ck }, are non-decreasing, (1.2.16), then find limg→∞…

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

A:

Q: Let {Ek}k=1∞  be a family of pairwise disjoint measurable sets. Then show that A satisfies m*(A∩(…

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

A:

Q: e. If x is a subset of V of cardinality 2, then f (x) is the edge connecting the two vertices in x.

A:

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: Let S1, S2 and S3 are disjoint measurable sets then: 3. 4" (S,uS,uS;) = (S) %3D 1=1

A: Solution  True Explanation :-

Q: 4.Describe the largest set S on which it is correct to say that f is continuous S (x,y) = In(1–x² –…

A: Given problem:- Describe the largest set S on which it is correct to say that f is continuous C.…

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls

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Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: 3. If is a collection of dosed sets in R such that every finite subcollection has a nonempty…

A: Given : θ is a collection of closed sets in ℝ such that every finite subcollection has a non empty…

Q: Which of the following sets spans R°? None of these {(-3,0,2)} O {(-3,0,2),(5,1,0),(0,1,1)}…

A: The solution is given as

Q: 1. Show that x is a regular patch.

A: given Xu,v=u2-cosv , u+sint , cosv show that X is a regular patch

Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…

Q: Show that if E is any measurable set, then -v (E) < v(E) < v*(E) and |v( E)| < \v|(E).

A: