10/1A1 Let X= 2* and T-³A≤X: A finite sot) does T form Set topological structure over X B Let X+0 and X.EX fixed Point So does T-{A=x* x₂€ A} form a topological structure over X

Q: Let τ and τ' be two topologies of a set X. Is the family τ∪τ' formed by the open elements of both…

A: Union of two topologies is not necessary a topology.

Q: True or False? 11. If Γ = {[0, 1/n) | n ∈ N} then ∩Γ = [0, 1). 12. Let R be a relation on a set A.…

A: 11) if Γ ={[0,1n) | n∈N}  then ∩Γ=[0,1)         Γ= {[0,1), [0,1/2), [0,1/3), [0,1/4), [0,1/5),…

Q: 16. A topological space (X, t) is Lindelöf if every open cover of X has a finite or countably…

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Q: 2/E5Limf)=3-5 and Lim fo=65 メー→2 the function has a double sided limit oronsided Limit 2

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Q: 1 - Let A = {x € R: -2-4<x<5+0} B = {x € R: x²(x+y+1)x < 0} Find the set AUB,ANB, A\B, B\A A', B' as…

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Q: Theorem: If R is a fuzzy relation on the set X, then (R-1)-1 = R

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Q: Let Find a spanning set for the null space of A. 6 - [º A = 3 3 -2 -3] 2

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Q: (16) Let A = 1 3 3 2 1 Find the spanning set of Null (A). 1 2 2 1 1

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Q: Theorem 9. The following statements regarding the set E are equivalent: (i) E is measurable. (ii)…

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Q: 25. For any set S CR, let S denote the union of all the open sets contained in S. (a) Prove that S…

A: The given question is solved below.

Q: F onto a subfield of an algebraic closure F Theory 9. Let Z2 be an algebraic closure of Z2, and let…

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Q: 1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show…

A: Given: Set: X=x∈ℝ4 / 93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1To Show: b) ConvX is a…

Q: SUPpose that. the functins f and q are difined ·as follows, FCX). =x -z g (x) = Aind Ź then, give HS…

A: We can find the answers as below.

Q: show that (0.1)with usual topology is connected

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Q: 1) (b) (c) Consider the set X = {x € R¹ / 93x1 +34x2 + 26x3 + 18x4 ≤ 131, x1, X2, X3, X4 € {0, 1}}.…

A: Given: Set, X=x∈ℝ4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1We need to show that the valid…

Q: 12. A path is said to be closed if the function that generates it satisfies f(0) = f(1). Show that…

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Q: EXERCISE 2: For each a/ and b/ answer these questions: (i) Sketch the set of points (directly, no…

A: (i) The parts shaded in yellow gives the required region defined by (a) (ii) bounded (iii) closed…

Q: Let A = {Ba: a € A} be a family of sets and let G be a nonempty set. Prove Gn an (UB.) - U(GOB₂) =…

A: Given: A=Bα : α∈∆ be a family of sets and let G be a nonempty set. To prove: G∩∪α∈∆Bα=∪α∈∆G∩Bα

Q: According to the Root Locus rules: O A) Root Locus starts at zeros the of G(s) and ends at the zeros…

A: The root locus is used to predict the behaviour of the closed-loop system.

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

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Q: Determine (without proof) the suprema and infima of the following sets: (a) {n € N : n² < 10} (b)…

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Q: (a) Find the value of x such that 61, = 133, (b) M and N are two intersecting sets. If n(M) = 20,…

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Q: For every element r in A, there is an element y in B such that (x, y) is in F. Can you please…

A: Relation: The relation from a set A to a set B is a subset of Cartesian product A×B. Function: The…

Q: 2- Find the set of lower bounds and the set of upper bounds of the following sets in Q, if it…

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

Q: :-(-1)" : n € N. State without proof the values of inf D (a) (i) Consider the set D = and sup D.…

A: As per the guidelines I am answering the only the part (a) of the question. For rest questions…

Q: 1- Find the set of lower bounds and the set of upper bounds of the following sets in R, if it…

A: Since you have posted multiple sunparts of a question so according to our guidelines we will solve…

Q: Consider relation R={(x,y)|x divides y,xEA,y€A} on the set A={2,3,4,5,10,12,25,30}. (a) Check…

A: We are given a relation : R={(x,y)|x divides y,x∈A,y∈A}  on a set A={2,3,4,5,10,12,25,30}

Q: Def (Function): A binary relation RCX X Y is called a function from X to Y, written f:X →Y if -…

A: The concepts have been explained with examples.

Q: Let Ki LiM sets be piver. M=knL =>(K XK)n(LXL)=MXMM Shaw.

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Q: 11. lim x→ー4 x2-16 2x2+9x+4 z2-36 12. lim Z--16 Z-6

A: (a) We have the given limit problem as limx→-4x2-162x2+9x+4 On calculating the factors of numerator…

Q: Q2. Answer as true or false: (a) f-'((AUB)nC) = (ƒ-'(A)n f-1C)) U (f-1(B) n f-1(C)). (b) Given the…

A: (a) is True. (b) is False.

Q: Find the geneval and Paaticular solution of the tollowing linear ODE IVP and do detailed cunve…

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Q: (a) By contradiction, prove that V r, y € Z, if ry is even and y is odd then x is even. (b) Show…

A: (a) Given v x,y ∈Z,     &amp; xy is an even integer with y is odd.     To show x is even.      Let…

Q: I.A) Antisymmetric Relation * A relation R on a set A is called antisymmetric if vavb((a,b) ER^…

A: I. Here, we have to select the best answer for each item. I. A) Antisymmetric Relation. I. B)…

Q: span (EE-EE) 3 O 2 O (A) and (B) O (A) ... = span Neither (A) nor (B). (B)... = span (4-6-8) 2 3 2 5…

A: Given that, span121, 031, 004, 152 We have to find the equivalent spanning set.

Q: write the equation for the quartic funtion ehich has zeros at -4, 1 and 3 (order 2) and passes…

A: According to the given data, find the equation: