i) show that a closed interval is a closed set;

Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

Q: Let W = (-∞,∞) be the universal set and Q = [-3,7) and P = [-5,4]. In interval notation, determine…

A:

Q: Give an example of a set that satisfies the condition, or prove that one does not exist: An…

A: The statement or condition :An infinite intersection of non-empty closed sets that is empty.

Q: HW4: Prove that U={x| x0 (1) explain why r_p>0 here

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A:

Q: Give two sets that are equal. Prove that they are indeed equal by using the "Axiom of…

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Q: Give an example of a set with a finite number of points that is not se-quentially compact, or else…

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Q: Provide a counter example that infinity intersection of open set is open

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Q: Give examples of three relationships that show all possible combinations of minimum and maximum…

A: We need to give examples of three relationships that show all possible combinations of minimum and…

Q: 1. Let A = [1, 3], B = (2, 5], and C= {2}. Write the inequalities (or equalities) that specify each…

A: We will just use of definitions of different type of sets

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Give example open set is compact

A:

Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: 6 All open sets are bounded.

A: Some times true

Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: Identify which sets are equal A = {0,1,2} B = {x ∈ R | -1 ≤ x < 3} C = {x ∈ R | -1 < x < 3} D =…

A: We identify which sets are equal.

Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: Define and give examples to all : what is bound sets ? what is the upper bounds ? the lower bounds ?

A: Define : a . Bounded set.            : b. Upper bounds.            : c. Lower bounds.

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: Give an example of a bounded set that has infinitely many isolated points

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Q: union of a collectionm of connected sets that have a point in common is conne

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Q: Decide whether each set is a cut. Prove your answer (if Yes show all three properties of a cut are…

A: a) A={q∈Q / q&lt;8}b) A={q∈Q / q3≤8}

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: How to Apply the Archimedes'principle to prove that a set is empty

A: Consider the given information. the Archimedes' principle is defined as, Property states that for…

Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…

Q: I need help with this question It's about inequality notation.

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Q: Let A E R2x3, be R². Determine whether or not S = {x R³ | Ax=b, x₁ ≤ 0, x₂ ≤ 0} X2 sa convex set.

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Q: Which of the following sets, given by the roster method, is equal to the set below given in…

A: The objective of the question is to find the set that matches the set-builder notation {x belongs to…

Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

A: