Let B= ((p.4) e R p + =1}. (n) Show that B is NOT disconnected (b) Given that there is no continuous mapping B R. infer that R is not homeomorphic to R.

Q: 2 T= {(x, y): y = x2+4

A: The given relation,   T=x,y: y=2x2+4

Q: ove that there does not exist a linear map T: R³ → R³ such that range T = null T (or uivalently…

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Q: (a) Prove that f is a one-to-one correspondence. (b) Prove that ray AF is between rays AB and AE if…

A: (a) To prove that f is a one-to-one correspondence, we need to show that f is both injective and…

Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

A:

Q: 14. 3x-2y 10 3x 9x+4y=-50

A: To solve the below system of equations using the substitution method. 3x−2y=109x+4y=−50

Q: D: Remind that the set F of all functions from R to R is a vector space. 3. Prove that F = 0 E

A: Here the set F of all functions from ℝ to ℝ is a vector space. It has to be proved that F=O⊕E.

Q: 22Prove that the line X2l+2t y=ー+3t そ2 :2+4t is s perpendicular tou the plane X-2yrzz6

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Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 2)}.…

A: Given  T = {0,1,2,3} and the relation R is defined on T as follows R= {(0,1),(1,2),(2,2) }

Q: ii. Use the basic definition of complex integration to evaluate the integral I $, z¹ dz, where the…

A: Step 1: Step 2: Step 3: Step 4:

Q: consider the space generated by the set of functions {cos nx , sen nx} with ,n = 0,1,2, … show that…

A: We will prove  the given statement.

Q: a(x,y) Let G(u, v) = (5u + 2v, 5u+9v) be a map from the uv-plane to the xy-plane. Calculate Jac(G) =…

A: Given that be a map from the -plane to the -plane.The objective is to calculate .

Q: Given R = { (x,y) ϵ R | x^2 = y^2, x,y ϵ A } on A = {1, 2, 3, 4, 5}, which of the following…

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Q: 0 IS SU b) Let f be a map. from a space X ipto a space Y and 6 is a base for Y .show that f…

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Q: Let T:V U be a homomprphism then ker T={0}if T is one-one.

A:

Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1), (1, 2), (2, 2)}.…

A: The symmetric closure, R(s) is calculated using the formula, R(s)=R∪R-1 , where, R-1=b,a: a,b∈R .…

Q: a) Consider the following functional relation, f, defined as: f:R - R, f(x) = x Determine whether or…

A: (a).                                     Given :  f:ℝ→ℝ  by  f(x)=x2To check: f  is  one - one…

Q: Let R be the relation on R given by R= {(x, y) : xy > 0}. Is R reflexive? symmetric? antisymmetric?…

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Q: Determine whether the relation R on the set Z is reflexive, symmetric, antisym- metric, and/or…

A: Given: The relation ℝ on the set ℤ and x,y∈ℝWe need to check whether the given ℝ on the set ℤ is…

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: 1.T.2 Let V be the set of all twice-differentiable functions f : R → R satisfying f"(x) = f(x) – 5.…

A: Let, f and g be two functions in V.  Then,        f"(x) = f(x) - 5       g"(x) = g(x) - 5.

Q: Let F = Vf and f = 5x²y - 5z. Calculate F. dr for the path r₁ = (t, t,0), 0 ≤ t ≤ 1. (Give your…

A: We will use fundamental theorem of line integrals

Q: R= {(0,2). (1, 1). (1,3), (2, 1). (2, 2). (2,3 For relation R find the Reflexive closure; Symmetric…

A: Given:- Set A={0,1,2,3}   , relation R:A×A is defined as : R={…

Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

A:

Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: G1 is a semi-circle Y: = √4 - X² starting at (2, zero) ends at (-2, zero) while G2 is a directed…

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Q: 2. Let f A B be a mapping. Prove that f is bijective if and only if f(A\C) = B\ƒ(C) for all CCA.

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Q: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive relation

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

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Q: Let T: R2 R be a linear map such that T(x, y) = (2x, 3y, 2y- r), then one of the following in range…

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Q: Construct a one-to-on continuous mapping of the set {(#1, 12, - ..., In); 0 < T; < 1. j= 1, 2,…

A: Given that : x1,x2,x3,.........,xn, 0&lt;xj&lt;1, j=1,2,3,.....,n So we have to take ,…

Q: Let F: RP → RP be a differentiable map. Given u, v ERP, show that Du+vF = D₂F + D₂F.

A: