For sets A and B, prove that AU (B – A) = B

Q: A relation Ris defined on N by a R b if a/b e N. For c, d e N, under what conditions is c R1 d?

A: An inverse relation is the set of ordered pairs obtained by interchanging the first and second…

Q: Show by any valid method except Venn diagram that ((A U D) N B)n ((C U B) N A) = AN B. %3D

A: Given: A∪D∩B∩C∪B∩A We have to prove A∪D∩B∩C∪B∩A=A∩B

Q: Consider the set P = {f€C([0, 1], R) | ƒ is nondecreasing} Determine if (P,d2) is separable. Here,…

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Q: For each of the following sets A, B prove or disprove whether AC B and BC A a) A = {r € Z: Byezt =…

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Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: Give the condition which ensure that Je-| < 1 where z E C.

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Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: let H = {n² |n e Z*}, determine whether it is closed under

A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…

Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: of all Z € C that z iz e = e a Descnibe and sketch the set

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Q: Fix n ≥ 1 and let A be a non-empty closed subset of Rn such that if x, y ∈ A then (x+y)/2∈ A. Show…

A: The given details: Fix and let A be a non-empty closed subset of Rn such that, Show that A is path…

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: For each of the following sets A, B prove or disprove whether ACB and B CA a) A= {T EZ:yeza = 4y +…

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Q: Show that a set {V1, ..., Vp} in R" is affinely dependent when p > n + 2.

A:

Q: Find the Cartesian Product of the given sets:  With A = {c, d, f} and B = { w, x}, find B x A.

A: A = {c, d, f} and B = {w, x}, B x A = { (w,c), (w,d), (w,f), (x,c), (x,d), (x,f) }

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: 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: Let (X, T) be a topological Space and ACX- Develop the relation between Fr ( Fr(A)) and Fr(A).

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Q: lar, let m = 2 and n e of A and B such that

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Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

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Q: For sets A and B, define A+ B = {a +b: a € A, b e B}. (a) Prove that if A and B are open, then A+ B…

A: Given : A and B are two sets and a set A+B is defined as, A+B=a+b:a∈A,b∈B

Q: If f, g E R[a,b] with f < g on [a,b], prove that g.

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Q: Suppose S, T ∈ ?(V) are such that ST = TS. Prove that range S is invariant under T.

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Q: Let X, Y be sets and f : X →Y. Prove f"(A\B) = f"(A) \ f¯"(B). for any A, B CY.

A: Solution:Given:          X, Y    are the Sets and                      f: X→ Y To prove:  f-1(A \…

Q: .Prove that la + b + c| < |a] + |b| + ]c]

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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: For sets A and B, define A+B = {a + b: a € A, b E B}. (a) Prove that if A and B are open, then A+ B…

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Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Let V C(R ) be a nonempty open set satisfying a – b EV whenever a, b e V. Prove that V = R. %D

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Q: Let X be a nonempty set and fix x E X. Define (1, rE A (A) = 10, 4 A

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Q: For every ,x, y E R, let p(x, y) =| x² – y² |. Is p a metric -

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Q: Prove: If ƒ e R(a) on [a,b] and g e R(a) on [a, b] , then fg e R(a) on [a,b]

A: Given if f∈Rα on a,b and g∈Rα on a,b. We have to prove that fg∈Rα on a,b. Since, f∈Rα on a,b then f…

Q: Let T={(a, 0): aER}, then T is Borel algebra.

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

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Q: For any set A and B prove that: a) А - В %3D А - (ВПА) b) BC A' iff A n B = ¢ с) (А — В) U В %3D…

A: The given question can be solved as shown in step 2 and 3. As per the guidelines of bartleby I'm…

Q: (iii) If (X,r) is topological space, A,BCX. Prove that (a) b(A)=AA (b) If ACB, then d(A) ≤d(B)

A: First part Is obvious from definition of boundary points of a set.

Q: Let X, Y be two sets. Prove that X x YC P(P(X UY )).

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Q: Prove that: If f E Ra, b), then |fI E Rla, b) with

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Q: Let X = {a.b.c.d.e) Find the topology r on X generated by f-{{a.b.c).(b.c.d).fc.d}}

A: X={a,b,c,d,e}

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

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

Q: Find all maps ¢:(Z,+) → (Q*, ×) satisfying O (a + b) = ¢(a) × ¢(b) Va, b e Z

A: We derive the function from the given properties.

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: (b) Let (X, >, ) be a measure space. For A, Be ). Show that μ(AU B ) - μ(Α) + μ(Β) -μ(An ). %3D

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

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: Sketch the set of all points (x, y) such that x + y| < e*.

A: Consider the function x+y≤ex. An absolute function is defined as x=x if x≥0-x if x&lt;0. So, there…

Q: Consider the set R. Prove: (i) VxER, x 0 = 0;

A: To prove: For any x∈ℝ, x·0=0.

Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)