4. In each case, sketch the closure of the set: 1 (c) Re (d) Re(z?) > 0.

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: e following sets of points is collinear 2. L(-5,13), M(-10,10), N(-20,4)

A: Here we have to prove that each of the following sets of points is collinear.  L(-5,13); M(-10,10),…

Q: A(n)................................... is the collection of all points in the plane such that the…

A: We know, A parabola is a collection of all the points in a plane such that the distance from each…

Q: 21. Let A and B be two on-empty bounded sets of positive embers and let С%3D {ху: х€ А and y € B}.…

A:

Q: Consider the reglon bounded by the graphs of y- and y- VE

A:

Q: Consider the set P = {f€C([0, 1], R) | ƒ is nondecreasing} Determine if (P,d2) is separable. Here,…

A:

Q: Solve the Ssy stem by graphing. S2x+3y=6 he+ hei-ニsっ What is te soloution set?

A: We have to find the solution set of the given equations when they represents a graph. A solution set…

Q: Suppose that l is a line. Let H be one of the two half-planes bounded by l. Give a proof that l U H…

A: Answer is mentioned below

Q: Find the limit point of the open interval (a, b) in IR, where a

A: We have to find the limit point of the open interval a, b in ℝ  where a<b. Limit point: Let S be…

Q: EX: Show that the telation ? >' is PartiaL oldering set of Por R-

A:

Q: O Show that if Si and S2 are convex sets in R™X", then so is t mxn S = {(x, y1 + y2) | x € R", y1,…

A: Convex set: , If a and b are points in a vector space S. Then the vector space is called convex set…

Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: 4).ェ Pare subset, -f y such that CeD than fic) is not eD, then the Convers %3D そイue.

A: Solution As it's mention C=D and f^-1 same , so each and every element from  f inverse we get equal.…

Q: The continuous image of a connected set is connected. That is, if X is connected and f: X→ Y is…

A:

Q: 1. Sketch the following sets and determine which are domains: (a) \z – 2+ i| 1; (e) 0 4; (d) Im z =…

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

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is 9 an…

A: Let (M,d) be a metric space and let S⊆M. A point a∈S is said to be an Interior Point of S if there…

Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

A:

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: How many points need to be in a set in R° to guarantee that the set is affinely dependent? А. 11 В.…

A: According to the given information, it is required to tell the number of points in a set R9 to…

Q: Find the image of the infinite strip <ys under the trans-

A:

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: Consider the sets X = {(x, y) E R²: x² + y² ≤ 1) and Y = ((x, y) = R²: x ≥ 0]. Sketch on R²the sets…

A:

Q: At Lana's bake sale, 2/3 of the brownies were purchased by 5/7 of the customers. If there were at…

A: Let X be the number of brownies and Y be the number of customers. It is given that 2/3 of the…

Q: If the conditions of the fixed point theorem are not satisfied, then there exist no unique fixed…

A: The ciric theorem states that, Let X be a complete metric space, and let f : X → X be such that,…

Q: C.1 Let r > 0 and define the closed ball by B,(x) = {y € X : d(x,y) <r} Show that B(x) is closed set…

A: Given: τ=B⊆X : ∀x0∈B, ∃rx0&gt;0, such that Brx0x0⊂B is a topology in X. Open ball Br(x)=y∈X : d(x,…

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: 12) Show that D- d-del is shortest distance betueen a x- by +c2.of ; and ax+by tcz= dz?

A:

Q: Let the non-empty set S {x-y3:x,y E R}, show that S is closed'under multiplication then find the…

A:

Q: The set R- {0} with the usual metric is connected.

A:

Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

A:

Q: A(n)............ is the collection of all points in the plane the sum of whose distances from two…

A: It is given that,   A(n) ............ is the collection of all points in the plane the sum of…

Q: Consider the number line R with the topology t = {Ø, R, (-0, a); a E R}. Is the set A = (-3, 0]…

A:

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Prove that the boundary points of an open interval (a, b) CR are the points a and b.

A: A point a∈ℝ is said to be boundary point of a set A⊂ℝ, if Ba,r∩A≠∅ and Ba,r∩Ac≠∅ for every…

Q: has

A: We have to choose the correct option from the given options according to the given information

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

A:

Q: 6. The distance between a point x ER and a nonempty set A CR is defined by d(x, A) = inf {\x – y| :…

A: In this question, we have to prove that d(x,A)=0 iff x belong in closer(A)

Q: X be a limit point of set ECR, then every o infinitely many points of terval containing

A:

Q: {S := n(x, y) | 2x + 3y ≥ 12}

A: First we draw the line then find the region.

Q: Let f : (X,d) - (Y, d1) becontinuous fumction, then for any closed set G in X, f(G) is not necessary…

A: False

Q: Evaluate: (In(2x-1)- ♫ − ( ²¹ ) + 25) da - 2 Limits: [1, 6] Using Trapezoidal, n = 30

A:

Q: جليلة Let I = [= 1,₂1] ISR interval w that I is negligible Set.

A:

Q: Show that if ƒ′′&gt; 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

A: Given:

Q: Given the set T := {(x, y) ∈ R^2 : |xy| Less or equ 1}. Is T a compact set? Show your working. If…

A:

Q: Show that the feasible set X = {r: g1(x) < 0,..., gr(x) <0} is a convex set, if all the functions 9;…

A:

Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

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: 2. Does d(x, y)= (x-y)? define a metric on the set of all real numbers?

A:

Q: what is a phythagoras theorem?

A: Pythagorean Theorem has a right angle triangle.

Q: 10. Prove that the set H={[,ne subgroap of GL(2, R). For show that x HxcH but xHx+H. :9 GL(2,R),

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.