Consider the sets A = {x € Z*, x < 13 | x prime} B = {x e Z*,x < 13 | x even} C = {x € Z*,x < 13 | (6 | x)} What is the size of the set A U BU C?

Q: 2. Use an edge-counting argument to show that K, cannot be drawn on a 2-holed torus without edges…

A: Suppose K9 had a 2-cell embedding in the torus. Then, this embedding has v=9 vertices and…

Q: 5. Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E) %3D

A: This is a problem of Real topology, metric topology.

Q: By considering the collection of closed intervals {[1- 2+ :n € N}in R, show that the union of an…

A: Answer

Q: For the given set A, determine whether P is a partition of A. A = R ("All Real Numbers"), P =…

A: Here, A= R ("All Real Numbers") P={C" sub "y: y is an element of R and y &gt; 0}, where C" sub "y =…

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: 18 What is the size of the space stretched by the set {x, x+x², x³, 1 , x²} ?    a) 2nd  B) 34…

A: Solve the following problem

Q: • Show that if D is a set and E is a closed set containing D, then E must contain ƏD, i.e., the…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Explain whether each of the following sets is countable or uncountable.  A= {x∈Q|−100≤x≤100}…

A: A= {x∈Q|−100≤x≤100} This is the subset of Raitional Number. And we know that Rational number Q is…

Q: 2. Sketch the following sets. Determine whether each set is open, closed, or neither and whether…

A: We will solve three subparts of the given problem as per the answering guidelines. If you want…

Q: (ii). Prove that a set S CR is everywhere dense iff it intersects every non-empty open sets in…

A:

Q: Find the extreme points and directions of the following polyhedral sets. а. S = {x:x +2x2 +x3 <10,-x…

A: Hi! As per the norms, we will be answering only the first one. If you need an answer to others then…

Q: 21. Let A and B be two non-empty bounded sets of positive numbers and let C = {xy : x e A and y e…

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Q: For a poset with the following Hasse diagram, consider the set {b, e, f}. The least upper bound of…

A: using the concept of upper bound least upper bound in hasse diagram...

Q: Can a set and it's Complement be both nowhere dense in R? A Ac=R-A

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Q: Consider sets A = {n E Z:n is odd} and B = {n E Z : n = 7k for some k E Z}. Prove that A and B have…

A: Prove that A and B have the same cardinality.

Q: Let M and N be nonempty bounded subsets of R and let M + N := {m + n : m ∈ M and n ∈ N} . Prove that…

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

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Q: Let Y be an infinite subset of a compact set X ⊂ R. Prove Y' does not equal ∅.

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Q: Describe the following sets by roster method: Example (i) {x : x + 5x + 6 = 0, x e N} (iii) {x : 4x…

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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: A set SCR" is bounded if there exists k €R such that, for all x E S, || = VE, 0. What can you say…

A:

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: 3. Are the following sets countable or uncountable? Justify your answer with a proof. (a) {2" |n e…

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Q: Consider the collection of sets {Bn : n E N}, such that Vn EN, B, = {x € R : -n <a <n}. Find U B,…

A: We are given, So, B1 = { x ∈ R | -1 ≤ x ≤ 1},       B2 = { x ∈ R | -2 ≤ x ≤ 2},       B3 = { x ∈ R…

Q: 3. Using the definition of open sets, prove that an interval (0, a) is open where a > 0 is an…

A: (3) Definition of open sets: To define open set first we define an open ball For a real number x and…

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: ( Prove that the set {a E R2: a2 ... Prove that the set {a E R2: a2 not equal to 6} is open.

A: Let the set is A=a1,a2∈ℝ2:a2≠6 The objective is to prove that the set A is open.

Q: Let A, BCR be two non-empty bounded sets. Assume that for every x E A, there exists y E B such that…

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Q: a. Show that the null-space N(A) is a convex set. Is it true for every A?

A: As both questions are of different type,we shall solve first Que only. For other questions kindly…

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

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Q: Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable…

A:

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

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Q: A set L cR is convex if:

A: In this question, we have to find the correct option for the convex set L⊂Rn  here we use the direct…

Q: A set consisting of single point has measure zero .A O nonzero measure .B O open .C O none of…

A: We have to find the measure

Q: b) B = {(x, y) : x² < e*+3y < 5y + 4x},

A: The objective is to find the closure of the given set.

Q: 2. For any n E N, let G, denote the interval (-). Prove that each G, is an open set in R and each G,…

A: Here Gn=-1n,1n     so, G1=-1,1           G2=(-12,12)           ..           Gn=-1n,1n Since all Gn…

Q: Let {An : n E N} be the indexed collection of sets defined by 1 2, 2+ 2n An Prove that: nMeN An = Ø

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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 ?

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Q: 7. Which of the following sets are open, and which are closed? Explain your answers by sketching the…

A: A set is open if all points of this set are interior points. A point x belongs to a set A  is said…

Q: Prove that a set S⊂R is everywhere dense iff it intersects every non-empty open sets in R. Prove…

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Q: Prove that the open ball B(p, 8) = {x : ||x – p|| < 8} is a convex set. [Hint: Use the Triangle…

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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: Prove that if A and B are disjoint denumerable sets, then A UB is denumerable.

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Q: .Which of the following sets is countable and which is uncountable: A = {x |x = 2n, n e N} B = {x |…

A: We will find out the required values.

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: Let A, B, C be arbitrary finite sets from the same universal set U. - (a) Is it true that A - B C (A…

A: SOLUTION-

Q: Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E)

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Q: Given the class interval 78.49 – 86.72, the class mark is Blank 1, the class size is Blank 2 and the…

A: Given 78.49 - 86.72 The definition of the class boundary is: