(3) S° is the largest open set in M that contained in S.

Q: Why is F= {An = (1/n, 1), nE N;n>1}not an open cover of [0, 1]? Which points in [0, 1] does UAn not…

A:

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: The closure of (-co0,2) in the left ray topology is A) (-c0,2) [B) (-0,2 C) R D) O

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Q: 4. Describe the reflection(s) that will carry the rectangle onto itself. 10 -10-9 -7 01 -2 -6

A: Given: The rectangle ABCD. To describe: The reflection of rectangle.

Q: If S is a subset of T , then u* ( T) sµ* (S).

A:

Q: is absolutely and uniformly conyergent for all vlues of x an t in the circle 121 <B-¹

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Q: What property must the set (AU B) have if the statement below is true? [(aff A) U (aff B)] C (AU B)…

A: The given question has been solved below.

Q: Hw/ Find the foutier Seties of the periudic funtin %3D Ans/ 3. an-

A: According to question,Given Function,fx = x2,0&lt;x&lt;2π

Q: A plane P passes through the points P(3, –1, –4), E(2,7, –1), and G(-1,6, 1)

A: In this question, we have given three points P(3,-1,-4) E(2,7,-1) and G(-1,6,1) By using these…

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: Blank 1 is movement of a side of a preimage parallel to that side with respect to one other fixed…

A: We have to fill the blanks.

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: spectra of TT* and T*T are real and cannot

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Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: Question No. o6: Evaluate the where C is yectangle ahere vertices (o,0)> (x,0), (x.%), (0 , %).

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Q: Claim 3. Let A and B be sets. Then A = B if both of the following condi- tions are satisfied: . АС…

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Q: 4. Let A Sketch the collection of points Ar for i in the unit square.

A: Let A=1101. Sketch collection of points Ax¯ for x¯ in the unit square. Matrices maps a polygon to a…

Q: АР 1. Find the point P such that - АВ = r, where A(4,3, –2), B(-5,0,4) and r = NIM

A: As per bartleby guidelines, I can answer only one question. So, please repost the other two…

Q: Match the homeomorphic figures. ....F Prove or disprove the following: FA and R are pathwise…

A: Given:- (a)Homeomorphic figures     △.................. F  T.................. 0∞...................…

Q: If there exists open ball B (a, r) such that B (a, r) nG=Ø then a is not limit point of G

A: To check whether there exists open ball B(a, r) such that B(a, r) ∩ G= ∅, then whether a is not…

Q: et S be a nonempty subset of R and let k E R. Define kS {ks : s E S}. Prove if k > 0, en sup(kS) = k…

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Q: Suppose S and T are balls with the same center. Show that one of them must be a subset of the other.

A: It is given that S and T are balls with same center. Let the center of the balls be a. Assume that…

Q: 2 / The eanation rasine itis an e quation of acircle passing through the origin and center onthe X.…

A: Polar to cartesian conversion:

Q: 1 1 S = 0 0 11 the spanning set. ect one: True

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Q: Show that the points D(0, 3), E(−2, 7), and F(2, 9) are the vertices of a right triangle. mDE  =…

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Q: 3.3 Let r1 and r2 be distinct points in the metric space (S, d). Verify that there are open balls S,…

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Q: Question 3. Consider the usual topology U on the set of real numbers. Describe the relative topology…

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Q: If H is a subgraph of G, then show that dg(u,v) <dí(u,v).

A: A graph G illustrates how the vertices and edges are connected. Thus a graph is an ordered pair…

Q: Which of these best describes T?

A:

Q: 1. In R2, what is the dual cone V* if the primal cone V is V %3D {y1 (-3, -4) + у2 (1, -3) |у »3 0}

A: Given: V={y1(-3,4)+y2(1,-3)|y&gt;=0}

Q: Identify the coordinates of P' after a reflection over the x-axis. O (5, 1) O (-5, -1) O(-5, 1) O…

A: Given

Q: Theorem 2.6.9. If P and Q are two points such that P + Q, then there exists a point R such that P,…

A: Axioms used: 1. There is one and only one line that contains two distinct points. Given: Theorem…

Q: 1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= 0}

A: In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) I y &gt;= 0}

Q: Prove that A N (BU C) = (A N B) U (A N C) by giving a Venn diagram proof. Label your diagram(s)…

A: Venn diagram are pictorial representations of mathematical or logical sets of data as closed curves…

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: u* (B) = inf{l&|: is a covering of B by closed boxes} for all BcR" %3D صواب İhi O

A: I will use the definition of measure.

Q: 4. Select the sequence of transformations that maps triangle LAP onto triangle L'A'P'. Ay P'

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Q: k and Ĉ = к апd rs along the a ICorteeion

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Q: 2 Let A be a fixed nonempty subset of set X and I= {Bc X | A Z B}. Show that (X,I) %3D is a matroid.

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Q: Qsit Prove that the Centre of a gp îs noymal. of

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Q: 2. Let A = {1,2, 3, 4} and define R on P(A) – {0} by xRy if and only if x N y # 0. Determine whether…

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Q: Let K = Span{ t-t, 1+3t}, then dim K = %3D

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Q: Theorem 4P.1 There are exactly six lines in the four-point geometry.   proof the Theorem 4P.1 by…

A: To prove that in the Four point geometry , there are exactly six lines: the proof should be based on…

Q: IIC sUUset of R". tve R" and let k e R. Prove that S = {x e R":x.v = k} an affine subset of R". %3D

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Q: (1) Rxy(t) = Ryx(-t) is a symmetry property.

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Q: 2 Find values for a, b, and c such that is an orthogonal set.

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Q: 3. Find a minimally invariant set in (C, R) that contains the circle [2 -(1+21)| = 4.

A: It is given that z-1+2i=4. Note that, z=x+iy. Substitute z=x+iy in z-1+2i=4:…

Q: 3.3 Let 11 and ra be distinct points in the metric space (S, d). Verify that there are open balls…

A: