1.5 Prove that all the a-cuts of any fuzzy set A defined on R" are convex if and only if H.(àr + (1- 2)s) 2 Min[u,(r), µ,(8)] such that r.sN. A « [0,1]

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

A:

Q: Sketch the set S = {z:|2iz – 2 – 5i| > 2} and state clearly if it is open/closed/neither,…

A: Solution: The set is S=z:2iz-2-5i≥2

Q: any Hermitian positive definite matria A=M-N, + N is Hermition, and if it is positive

A:

Q: T-space X has no Question 1. Show that a finite subset of a accumulation points.

A:

Q: 1. Prove by Induction that the numbr f edges of Kn

A:

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

A:

Q: Find an example of a bounded convex set S in R2 such that its profile P is nonempty but conv P ≠ S.

A:

Q: Prove (sn) is bounded if and only if lim sup |Sn| < +∞.

A:

Q: Prove that 10. Let f(0) = 20 be the map of S periodic points of f %3D are dense in S.

A: From the set of reals R, choose a subset P such that each and every point of R lies in P or if you…

Q: Show that a linear map T:X-→ Y between normed spaces is continuous if and only if {Tx,} is a Cauchy…

A:

Q: Give the set of limit points A0 of a singleton A = {(5, 2)} on the plane R 2 with the discrete…

A:

Q: (10) Suppose that the transtormation given by u=2x-g is used on the н наад) A where D integrat…

A:

Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

A:

Q: 8.F. Ifx= (1, I, --- ,)€R", define x, by e that z- l, is a norm on R'. Prove

A: Given that x=x1,x2,..,xn and x1=x1+x2+...+xn. The objective is to find the whether x1=x1+x2+...+xn…

Q: Exercise 6.40. Let E be a nonempty subset of R that is bounded above. Prove that if a = sup E, then…

A: This is the question of topology.

Q: rcise: Prove that every finite set S of R" has no accumulation point.

A: Proof of the the given theorem is given as

Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

A:

Q: give an example or prove it doesn't exist j. an orientation on K44 which contains no sources or…

A: The given statement is,  An orientation on k4,4 which contains no sources or sinks but is not…

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: 4 Compute the orthogonal projection of u= 3 onto the line L through and the origin. projz (5) =

A:

Q: Find a norm for C([0, 1]), so that C([0, 1]) is not complete under this norm.

A:

Q: 4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.

A: Hello, thanks for your question but according to our guidelines I am answering just question number…

Q: Queshon 6) Compute the arthogonal projection of 8 onto the Line L through -S] and the origin. -6 LS.

A: We have to find the orthogonal projection of v on the line through P and the origin.

Q: T-space X has no Question 1. Show that a finite subset of accumulation points.

A:

Q: 5 Compute the valuc of G.dL for G= 2ya, with A(1,-1, 2) and P(2. 1. 2) using the path: (a)…

A:

Q: The random walk in one dimension is certain recurrent. at, for large n, u2n N de a proof, courtesy…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: let Chn),(t) be dearuences of bounded Inal lenvegas uni formly repectively Show functrons. on A Lo…

A: Given - Let hn, tn be sequences of bounded functions on A that converges uniformly on A to h, t…

Q: Prove that {4- ) is an open cover of (0, 4), but that this cover has no finite subcover. k=1 This…

A: The complete solutions are given below

Q: Suppose we use a 6-th degree polynom, PeW to estimete gox) = 2e* with data points (Xi,9(X;)) where…

A: As per Bartleby's answering policy, we can answer only one question. So kindly post the remaining…

Q: 9. verify that lx1l= max ilt)| defines. telasb] a on the Space Ccla, b]. morm Solution :-

A:

Q: 4. Use the least upper bound property of R to prove that every nonempty subset of R that is bounded…

A: Solution

Q: A chow that the wsonskian d es will neves become zex0 to8 all spal

A: Here we use the fact ex&gt; 0 ,for all real x.

Q: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

Q: 38 A system {x;}ien in a normed space X is called a complete system Span {L-1 a;X; : Vn EN, a; E F}…

A:

Q: (b) Let # ACR be bounded below. Prove that Inf (A) =-Sup(-A). %3D

A: Let A is non-empty subset of real number . Let A be bounded below then we have to show that  Inf(A)…

Q: 2. i) State the definition of a Cauchy sequence in a metric space (X, d). When do we say that (X, d)…

A:

Q: 9 Find the lies which degion bounded and area in in first eyuadrant 12-axis by Jine V= n=770 Give…

A:

Q: 8. Show that A is Hermitian if and only if A = B - C with B,C positive.

A: A is Hermitian if and only if A=B-C with B, C positive.

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximuma possible…

A:

Q: Let fiay)-y) . Find the equatn of the tngrt planeeface-F the pea,,2

A:

Q: 2. Use the Gram-Schmidt process to find the first four orthogonal polyno- mials satisfying the…

A: (a)Natural basis of P-3(x)=1,x ,x2,x3 we will build an orthogonal basic H-0,H-1,H-2,H-3 Apply…

Q: If fi and fa are two bounded and integrable funct ions on [a, b] and there exists a number >0 such…

A:

Q: a nonempty compact set of IR. sup Ke K. be

A:

Q: Sketch the graph of the convex hull of S. In R, let S =. :0sx<3

A:

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

A: Soution.

Q: 2. Prove that [0,1] and U-1 An , where A,= [2n, 2n+1] have the same cardinality. %3D

A:

Q: 4. Find the number of surjections from {1, 2, ..., m} to {1, 2, .. ., n} such that no element in the…

A: We have to find the number of Surjection from one set to another set.

Q: (8) A space X is connected space IFF every continuous funetion f:X → D, Where D-(0,1} with discrete…

A: a) Constant function

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.