Write out the following sets by listing their elements between braces. 9. {X :X < {3,2,a} and |X|= 2} 10. {X cN:|X|< 1} 11. {X :Xs {3,2,a} and |X| = 4} 12. {X:Xs {3,2, a} and [X|= 1}

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

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Q: Show that the subset of R2 given by {(x, y) E R² : xy 1, x > 0} is closed.

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Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: 2. If (x, y) → (x +3, y- 7)maps TUVWTO T'U'v'w', what is the algebraic description that will map…

A: Note: Multiple questions posted simultaneously, answer to the first question is given. If there is a…

Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: The volume of traffic for a collection of intersections is shown in the fiqure below. 40 X3 X2 20 90…

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Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: 18 What is the size of the space stretched by the set {x, x+x², x³, 1 , x²} ?    a) 2nd  B) 34…

A: Solve the following problem

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

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Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

Q: Let X and Y be two T, spaces, then X×Y. :is

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Q: Given sets X and Y. For x EX and for y E Y, we form the Cartesian produc X x Y := {(x, y) : x E X, y…

A: Given that: X={-1, 1}Y={-2, 0, 2}

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: 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: 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: Let R have its usual topology and let X = {a,b, c}. Define f : R –→ X by а, х

A: Given, ℝ have its usual topology and let X=a, b, c. Define f: ℝ→X   by…

Q: 15. Given nonempty-subsets of R², say Y1,..., Yn, let Y* = {E÷=1 Y; | Y1 € Y1,.., Yn E Yn}. Given p…

A: Given: Y*=∑j=1nyj | y1∈Y1, y2∈Y2, ..., yn∈Yn and, for any p∈R2 and nonempty subset Y⊂R2, vp,…

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

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Q: Find fxTy and f,, and evaluate each at the given point. (x, y, z) = x2y3 + 2xyz- 4yz, (-2, 1, 2) %3D…

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Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

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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: Write the following sets in the roaster form. (a) A = {x | x is a positiveinteger less than 10 and…

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Q: Let a,be Z-{0}. Then one of the following statements is false A)lf ax+by=1 with x,y eZ, then…

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Q: 5. If (x, y) → (x+3,y-7)maps TUVWto TU'v'W', what is the algebraic description that will map…

A: As per rules we will solve only first question: 5. Given that (x,y)→(x+3,y-7) maps TUVW to T'U'V'W'…

Q: and for the following situation Determine forulas for w=(z,y, ) 2=z (t), y=y(w, v, p), z==(v,p),…

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Q: O Gven rref(A), -[!!] and A represents for mation →R; Tlu)-Au. Imear trans- Ti R State all rectors…

A: How to calculate the range of the operator T, whose corresponding RREF of the matrix is…

Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

A: 1. Given: D⊂E⊂A then D=E    To Find: To whether the sets are connected.   Where z=x+iy           z…

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: Given that  The joint probability mass function of X and Y is  f(x,y)=(x+y)/21   , x=1,2,3 and y=1,2…

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

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: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: Solution: The joint pmf of X and Y is  fX,Y(x,y)=(x+y)21     x=1,2,3    and y= 1,2  The pmf of X and…

Q: {S := n(x, y) | 2x + 3y ≥ 12}

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

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: Let X = R, and M = {0}, then span (M) = %3D %3D OR O {0}

A: If, M = {0} then, span(M) = {0}

Q: Using the data from sections 2.15,2.16, & 2.19 show that these statements are true. (photos of…

A: Here,X are the observations for Eyes Level condition from 2.15 and Y are the observations from Eyes…

Q: #6

A: A function T; Rn → Rm is called a linear transformation if T satisfies the following two linearity…

Q: Theorem:For all Xiyiz,w EN i) X<y ^ z sw =)x+Z <ytw ii) xsy ^ zw =) x+Z< y tw )x<う tsw 1 Esw うメ+ と x…

A: Solution: We know that for x,y∈ℕ If x&lt;y then ∃k∈ℤ+,k&gt;0 such that x+k=y If x≤y then ∃k∈ℤ+,…

Q: If f(x 1.,„,) = g(ê,e) h(x,...,, then ê is Select one: a. efficient b. consistent C. unbiased d.…

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Q: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: 1. Prove algebraically that for any sets X and Y, we have Y – (Y – X) = X nY.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A subset W of R° is given by = {(x,y, z) | 2x = y = 2z}. (i) Write down the distinct elements of W.

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Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

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Q: (1) What is the relationshi etween lines 11 and 12? wl Y = 2 y = 1+ 2t Z = 1+t

A: Given: L1:x=2        y=1+2t     z=1+tL2:x=4-t   y=1+t      z=2+t

Q: 1. Let x, y, z€ R, w e R*. Also let a, b, ceZ and de Z*. For each of the following determine is…

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