Let A = (-2, 4)., and B = [0, 0). Choose sets that are infinite and uncountable. O B° \ A O Bº nQ O P(ANN) O P(AnQ)

Q: 3,Find the max, min, infledon Points an d the intervals eln which the F unc tHon on

A: f(x)=4x3+6x2-6x-4f'(x)=12x2+12x-6f'(x)=012x2+12x-6=02x2+2x-1=0 x=-2±4-4(2)(-1)2x=-1±32     (critical…

Q: (b) Consider the set R. Prove: (i) VxER, x 0 = 0; (ii) If x y = 0 then either x = 0 or y = 0, or…

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Q: التاريخ 27 أمر موح let I = (a,b) be an open interval show that - for every positive sM(IDS.

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Q: Show that the following pairs of sets S and T are equinumerous by finding a specific bijection…

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Q: 5. Which of the following sets S are polyhedra? If possible, express S in the form S = {x | Ax 3 b,…

A: Given set is S=x∈ℝn:x≥0, 1Tx=1, ∑i=1nxiai=b1,∑i=1nxia2i=b2, ai∈ℝ, b1,b2∈ℝ Clearly S is defined by…

Q: Let 0 E A CR. Show that if A is both open and closed, then A = R. (Hint: Let M = sup{t: [0,t] C A})…

A: We prove this by contradiction.

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: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

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Q: The dimension of the set W = {(2t – s, s, t) : s, t e R} of R is equal to: %3D

A: The dimension of the set W={(2t-s,s,t) : s,t ∈ R} of R3 x=2t-s y=s z=t (t,s) ∈ R   This can be…

Q: Use the given sets to find |X n Y. U = х, у, Y = {suav.e}

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Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

A: Solution:-

Q: Let A & M and μ*(A) < oo. st B₁, B2,..., BEC, k <co with Bin B „²(AAŬB₂) <« j=1 any two sets E₁ and…

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Q: What can you say about a set ACR, if every subset of A is closed in R? Which of the following…

A: Given: Every subset of A is closed in ℝ. To do: What conclusion can be given about A.   Conclusion:…

Q: Using a proof by contradiction and the well-ordering property, prove Vr E R, if 2 < r, then Vn E N,…

A: Every nonempty subset of natural numbers has a smallest element, i.e, if B is a nonempty subset of…

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: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

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Q: Assume that u E W%3 (R"). What is the largest q such that we can guarantee that u E Lº (Rº). O 30 7…

A: In this question, 3 is the largest q such that we can guarantee that u∈Lq(R10). Hence option third…

Q: C. Suppose that P and Q are points so that 0 < PQ < a. Prove the following claim: PQ C PQ C PO Note…

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Q: Given: OO, XW * WY Prove: arcs XZZY (Use paragraph proof) X Z

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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: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: If Do, D1,..., Dn... nEN, are dense open sets of reals, then the intersection D = 0 Dn is dense in…

A: Condition: Dn is the open dense sets of reals, for all n∈ℕ. To find: Intersection of infinite open…

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: 1. In the figure, E is the midpoint of (NS)¯and LSzZN. Which postulate justifies that APES = A MEN?…

A: Introduction: When two parallel lines are intersected by a transversal, the pair of angles formed on…

Q: Which of the following sets has oo in its interior: (a) {z = « + iy, x² 0} (c) {z = x + yi, |z +1|…

A: We have to find region bounded by given in equation and find which region goes to infinity  Here we…

Q: Use the given sets to find P U (Qn R). ..., X, y, P = %3D R =

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Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

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Q: If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ,…

A: Given P an Q are represented by the numbers z1 and z2 such that |1z1+1z2|=|1z1-1z2| We need to find…

Q: Use the given sets to find PU (Qn R). U = {ab.c.} = {p.ha.que} %3D ..., X, y, %3D q, u, %3D R = k,…

A: Given: P=p,l,a,q,u,e, Q=q,u,i,c,k,l,y, R=k,i,n,d,l,y according to given data Q∩R will be common…

Q: Let linear tiansformation I(4)=(2,32and Tls0) =(3B,2) Cheek whether T? exists or noti2 Find T. E=R…

A: The objective is to check whether inverse of T exists or not and find it.

Q: (a, b) is measurable. ulgn O ihi O

A: I will use the definition of measurable set.

Q: Let A, B be bounded subsets of R. Let A+B = {r+y:1 € A, y E B} and AB = {ry : 1 € A, y € B}. Which…

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Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: Let {C, : r € [0, 0)} be the family of indexed sets given by Cr {(x, y) E R : a? + y = r²} a)…

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Q: Write down an explicit bijection between the following sets a. The interval (-2,1] and the unit…

A: Given:-             Write down an explicit bijection between the following setsa. The interval…

Q: - Sketch the set S = {z: |z − 2 − i|≤2}. Find the interior, exterior and boundary set of S. Then,…

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Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

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Q: Let R be the set of real numbers and let B be the collection of all intervals of the form [a, b),…

A: Consider the provided question, Given that, R be the set of real numbers and B be the collection of…

Q: 5. Determine if the given sets are simply connected or not: 1. R? with the circle x² + y² = 1…

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Q: show that fo=Ixl is Conlindalus everyuhere

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Let 2 z, and Z2 = %3D ) show {2, ,2z} that or thonormal c's an set in O Write the rector as a 2 = -…

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Q: . Prove with the usual notations that: (b) A +V =- (c) A= SEŽ (a) EV = VE = A

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

Q: be such that Ca,m)=1, Let thE N and a,be Z Cb ,m) = ), and Cab, m)=\. Let j= Om Ca); k= Om(b) and n=…

A: Let m,n∈ℕ and a,b∈ℤ such that a,m=1, b,m=1 and ab,m=1 Suppose j=Oma, k=Omb and n=Omab Again, let…

Q: Assume f,g : [a, b] → [c, d] where a < b and c < d. Prove that sup{f(x)+g(x) : x € [a, b]} <…

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Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x

Q: y (b, f (b)) (a, f (a))

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Q: Let S be a bounded set in R and. let a > 0, and let aS := {as : s E S}. Prove that: i. inf(as) = a…

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Q: Show that the following pairs of sets S and T are equinumerous by finding a specific bijection…

A: Equinumerous Sets:- Two sets S and T are called Equinumerous Sets if there exists a bijection (one…