Give an example of sets S and T where P(SUT)メP(S) U P(T)

Q: Suppose that X,Y and Z are subsets of {1, 2, 3, . . . , 10} and |X| = |Y| = |Z| = 7. (i) Prove that…

A: Given that X,Y,Z are subsets of {1,2,3,...,10} |X|=|Y|=|Z|=7. X∪Y≤10 i)X∩Y≥4 X∪Y=X+Y-X∩YX∩Y=X+Y-X∪Y…

Q: j) A U A = A k) A U $ = A

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Q: 1.* Let U C R? be an open and bounded set and u e C²(U) n C(U) satisfy -1 Ди(х) : in U. 1 + |x|

A: Since I have solved similar ones, Let us show that u attains its minimum on the boundary

Q: Use the element method and contradiction to prove that for all sets S and T S Ռ ( T - S) = {  }

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Q: 2 Let F be a closed set for k = 1, 2, ... , n in (S, d). Show that |J F, is closed. k=1

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

Q: 8. Sketch the sets X = {(x, y) e R :x+y s1} and Y = {(x,y) ER:-1sys0} on R. On separate drawings,…

A: And,

Q: Complete the proof: If A≤B and B≤C, then ACCn(transitive property for set in inclusion) Need to…

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Q: [3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:

A: Let S be a nonempty convex set in Rn, and  Let f:Rn→R be defined as follows:…

Q: Queston2 {e-x, xe-O onlo, c∞) a) shau that q fandamented Set

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Q: Prove that the set {a E R: a2 not equal to 6} is open.

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Q: H.W: Let X = {0,1,2, ... ,10} and let A, B be fuzzy sets in X such that %3D A = {x € X is neither…

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Q: Which of the following sets is linearly independent in P2 ? {1+x + x?, x – x²,x + x²} the above set

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Q: O Show that if Si and S2 are convex sets in R™X", then so is t mxn S = {(x, y1 + y2) | x € R", y1,…

A: Convex set: , If a and b are points in a vector space S. Then the vector space is called convex set…

Q: In a Cofinite topology of X the collection of subsets a) r = {AcX|A ±Ø or A is finite} b) r = {Ac X|…

A: Let X be a non-empty set, then the collection of subsets of X whose complements are finite along…

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

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: For all sets A , B and C A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C )

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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: 3. (a) Prove that A\(BnC) = (A\B)U (A\C) for any sets A, B, C

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The relation - on the set A = Z x (N - {0}) by (u, v) - (z, w) if and only if wu = zv. Specify the…

A: We will use the relation wu=zv between two elements (u,v) and (z,w) .

Q: 8. Sketch the sets X = {(x,y) E R :x +y s 1} and Y = {(x, y) ER:-1sys0} on R. On separate drawings,…

A:

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: Exercise 1. Prove that for sets A, B,C we have C \(AUB) = (C\ A) N (C \ B).

A: We have to show that for sets A, B, C   C ∖(A∪B)=(C∖A)∩(C∖B).

Q: (b) = R°, W is the set of all (x1, 22, 13) such that 2xi = -x2+ X3. (c) V = R³, W is the set of all…

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Q: Prove that P(Sn T) P(S) n P(T) for any sets S and T

A: Let, S and T be a any set. also, P(S) be any power set of S and P(T) be any power set of T.x∈P(S∩T)…

Q: let U and y be bounded sets. if u er i tre M+ (V) ≤M₂ (V) and M^ (U) SM³ (V) 1

A: Given :  U and V are bounded sets with  U⊆ V. To show :  m*(U) ≤ m*V  and  m*U ≤ m*V,  where m*U and…

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B) n (A x C)

A: we have to prove the lemma .

Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

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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: Prove that if R, S, and T are nonempty sets, then R×T ⊆ S×T if and only if R ⊆ S.

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Q: Let A and B be sets. Let X = A n B, Y = A \ X and Z = B\ X. Prove that X n Y = Ø, X n Z = Ø, Y n Z =…

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Q: 5. Suppose f E L'(R²) is real-valued. Show that there exists a measurable set EC R? such that fdm2.…

A: Given that f∈L1(ℝ2). And E⊆ℝ2. The objective is to show that ∫Efdm2=∫ℝ2/Efdm2.

Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

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Q: Identify all nonempty set/s from the following A = {x|x € N, 2x + 7 = 3} B = {x|x € Z, 2x + 7 = 4} C…

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Q: let A Set bounded below, ילC erove that C. nf A inf C A %3D

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

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Q: Sets F and G are defined as follows. F={e,f, g} G=(a, b, e)

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Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

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Q: Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following   must…

A: See the detailed solution below.

Q: Let S be the subset of the ℝ2 given by all pairs (x, y) so that x2 + y2 = 2. Show that S is a closed…

A: Let, s be the circle given by, s=x,y∈ℝ2 :x2+y2=2  Then s is a closed subset of ℝ2. Let us consider a…

Q: let E be a set that baunded. Prove that Inf E = Sup -E) where R, XE E y

A: To prove for a buonded set E inf(E) = -sup(-E) , where -E = {-x, x belongs to E} , we first prove…

Q: (iii) The outer measure is translation invariant i.e. for every set A and for each x = R, m* (A + x)…

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Q: Three fuzzy sets are defined as follows: 0.1 0.4 A- 30 60 90 120 ***** 班,班。 B- 0.5 0.7 0.3 0.33 0.65…

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

Q: 3. Prove if x is an isolated point of a set S, then x E bd S.

A: Since you have posted a multiple question according to guildlines I will solve first question(Q3)…

Q: Give an example of (v1, V2, V3) and (W1, w2, W3) independent se- span(wi, w2, w3) and {v1, v2, v3}(…

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Q: 4.2 Let Fj, be a closed set for k = 1,2, ... ,n in (S, d). Show that U Fk is closed.

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