ki(x, ele), ) bea be a Boral mea sure Space Suppose that ŷ An obd be afumily of lements of BiR) Show that A, c Az CAg un C An C then evaluate MIU.

Q: Prove that for any sets A, B, C: (AUB)-B A - B

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Q: 4: Ex 4.) Let S be a non empty bounded set in R. a ( a. Let azo, and let oS := {as: SES}. Prove that…

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Q: U.S.) A (US₂) = VUSIAS₂ s₁tx, √₂ +₂

A: Given information: S1, S2 be the non-empty collection of sets. To show: Distributive Law union over…

Q: * Let R be the usual space." In R, if A = [-5,0) U N, then Bd(A) = N O [-5,0] O [-5,0) O [-5,0] UN O…

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Q: Shafe froe fabe, oting your ener. or The sef of natural nurnkers Bith the cwuel metir is compact of…

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Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: b) Let be a set of integers and T={o}{U,,ne N), on N. Show that whether (N,T) is 1) T₁-spr.ce or not…

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Q: Write the absolute value function in standard form for the giving graph use a or B as directed

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Let Xis Hilber - Ⓒ || T* ace 2 T* || =)) + |1²

A: This is a problem of Functional Analysis.

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

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Q: Q/ show thet f(2) = 2+ Conformal maps 121= 1 ? on

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Q: Question 2. Let (X,r) be a topological space and let A be a subset of X. Determine whether the…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Find, the domain of each of these, ped pred cates where the doman is the set of untegers లు రుంకు

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Samas (:])-[-] - (M)-[:] L (1) a) why do you know as compute given. {0.00} solve using system…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 1$ A and B are positive semide are Lal allnegative all non negatie El gllpositve y noneofabove

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Q: şa,6şc2.Debine a selation I on. pl2) which satisfies. For all set A and B in P(X) AJB ANB+

A: Given x={a, b, c}P(x)={ {a} , {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}, ∅}a relation onJ: P(x)…

Q: Ex 4.) Let Sbe a non empty bounded set in 1. aj Let azo, and let a S:= {as: SES}. Prove that inf…

A: Let S be any -empty bounded set in a) Let  , and let  Since,   is a bounded subset of , Sup and Inf…

Q: on 'N" en Prove Delween Aborms is lenre equala bub

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Q: Let lx, T) be a topological Space and A, B S X- if A is open, then show that An CIIB) s CLLANB). if…

A: Given X, τ be a topological space and A, B⊆X. Suppose, A is open then An arbitrary x∈A∩clB implies…

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: Homework: Determined whether the following sets are open or closed in (IR", ||. |I): 1) [a , b1] ×…

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Q: 5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that…

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Q: The shaded regions below represent the set {(x, y) | P(x, y)}. This means every point in the shaded…

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Q: 3) Let S be o st defined os follow s: 05 Deter mire ue ther S is o con vea set or not.

A: We have,  The set C is said to be convex set if for any u,v∈C, the point tu+1-tv∈C for all t∈0,1…

Q: $ 6)==x-2+* ad Find all y and y-interacpts, if they exist ) Findt all relative extema, if they exist…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: W Sketch the Locus of those points w With 41 | W ²-2 W-1|=0 w 4) R₁ [11-4)²] = 0 c) Re[*/*²)] = 0

A: As per the question we are given the following equations in complex domain ℂ and we have to sketch…

Q: 3) let X be discrete topology and Ac X, find A ?

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Q: 1) let (X, T) be a topological space and A, BEX. In this case, show the following a) = 0 а) бала " a…

A: Given that X, τ is a topological space and A, B⊂X . To show: (a) if A is open , then ∂A∩A =ϕ…

Q: Suppose Ak,., A2 , A1 and B are points on R" Prove that if {A1 , A2, .. Ak} is an independent linear…

A: proof :- A1,A2,...Ak are linear independent set ⇒c1A1+c2A2,...ckAk=0  where c1=c2=...=ck=0…