QUESTION6 Let E = (3, + o )U(-1, 3) u{-4}, then the interior of E is v, the boundary of E is and the closure of E is

Q: Q2) Let (A,T)be topological spaces; i=1,2,3. Then A, x A2 x Az is homomorphic to (A, x A2) x A3 I

A: Definition : Let X and Y be spaces, and let B be the collection of sets U × V , where U ⊆ X and V ⊆…

Q: 1. Let A = {a, b, c}, B = {1,2,3}, C = {x, y, z, w}, D = {4,5, 6}. Let the functions f : A → B, g :…

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Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: Show that if (xig)m.u. is re<rz , it is 8\x,r) C Blxirs] for Jx EX.

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Q: Let f(x, y) = (2x - y,x-2y); (x, y) E R x R, (R is set of real numbers.) %3D a) Show that f is one…

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Q: 4. Let A and B be sets and let T C B. Also let f : A → B. (a) Use a diagram to show that f(f-'(T)) C…

A: According to the given information,

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

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Q: Let U, A, B, and C be defined as shown below. U= [ a, b, c, d, e, f, g, h, i, j } A = { d, e, g, h,…

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Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Does S={(1,0,1),(2,1,0),(3,,1,1),(1,1,1)} spans R³ ? Select one: O True O False

A: Given: S={(1,0,1),(2,1,0),(3,1,1),(1,1,1)}

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

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Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: Example 9. Classify each relation as constant, linear, quadratic, or neither. a) y = x² + 5x + 6 b)…

A: The solution is given below:

Q: 9. S= {(6,2, 1), (-1,3,2)} is: %3D linearly independent set of R. b. a linearly dependent set of R3.…

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Q: Let U= {1, 7, 2, 12, 5, 10, 20, 18} A = {1, 20, 18} C = {7, 2, 12, 5, 10} Find A U C'.

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Q: The universal set is U with n(U)= 70, A and B are subsets of U with n(A)= 55, n(B)= 20 and n(A’…

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Q: If |ū| = 4, |v|=5, |ū-v=6, determine |ū+ v.

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Q: Which information about the coordinates of G and H prove that GH is the midsegment of ΔΑΒΟ? H В(3,…

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Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

Q: Which of the following points is closest to (1,0, 1,0, 1, 1) using Hamming distance? O (1,1,1,1,1,0)…

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Q: (b) If WCU, prove that (Recall that U+W = (c) If U + W = U, prove that WCU. U + W = U. = {u+w|u€ U₁w…

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Q: Prove that u × 0 = 0 × u = 0.

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Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: If G,=(-,1), then {G„}n€Nis a countable open cover of (0,1) .A O (a cover of [0,1.B O not an open…

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Q: Find the value of y, given the value of x. 11 a) Cari nilai dy dengan nilai x yang diberikan. de de…

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

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: Let $(u, v) = (u², v). Find the following images under (a) The u-axis O the positive x-axis…

A: Given, Part a)  i) To find the image of u-axis under Since the v coordinate of points on u axis is…

Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are…

A: Solution ::

Q: Show that if (x.g) m. is re<rz, it is 8lx,r) C Blx,g) for x Ex. U.

A: Metric or Distance: A metric or distance is a function ρ :X×X→ℝ such that ρx, y represents the…

Q: on 1: a) Let O be the set of odd numbers and O' = {1,5, 9, 13, 17, ...} be its subset. Define the…

A: Since the part b is independent of the first part so I am answering the first question only for the…

Q: Q3/ Let X = (0,1,2,...) and T = (0) U (Un.nE N), where Un = {n, n+1,n+ 2,...), show that whether…

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Q: Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,511.9 miles. The…

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Q: |U( Z Ð Z O Z O Z)| is: O 2 O 16 8

A: We have to determine the number of units in the given algebraic structure.