Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C), that is, (x,y) = A x (BUC) = (x,y) = (A x B) U (A x C).

Q: Consider V = {(2,y) : x, y ≤ R}. Let and ⋆ be operations on this set defined in the following way:…

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Q: 1 Determine whether or not the three given points le on a ne A (1,1,2), B(-1,-9, 3), C (3,2,1) 2.…

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Q: Method of algebra and cite a property used for every step: (Z − Y) − (Y − X) = Z − Y.

A: To prove: (Z − Y) − (Y − X) = Z − Y

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

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Q: Let S = {(r.y) R²: (x-1)² + y² ≤4 and y> √3}. Question a. Find the interior, exterior and boundary…

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Q: Let A = {1, 2, 3, 4, 5}. Define the following relations on A. R1 = {(1,1), (1,2), (2,1), (3,2),…

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Q: Ο b. (ΧΔΥ)ΔΖ - ΧΔ(ΥΔΖ)

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Q: Consider the set V = {(x, y) = R² : x+y=1}. on this set defined in the following way: (x2, y2) = (x₁…

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Q: Consider the following sets A = {x |x > 1}, B = {x E N|1< x < 3} and C = (-2, 2). %3D 1. Find: (а)…

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Q: 1. A x (BNC) = (A × B)n (A x C). X

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Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

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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: get the following sets {(x, y) : x ∈[1, 2], y ∈[1, 2]} and {(x, y) : x = 2, y ∈[0, 1]}

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Q: Establish formally, whether the following set is open, closed, or neither closed nor open (justify…

A: We will use the basic knowledge of set theory and point-set topology to answer this question…

Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

Q: 1. Prove that for all sets X, Y , if XU Y = Xn Y, then X = Y. %3D

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Q: For sets A and B, prove that AU (B - A) = B

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Q: 16. Let vo = (a, b) and let v = (x, y). Describe the sets of points in R? satisfying the following…

A: Given v0=a,b, v=x,y

Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

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Q: Is the set {(x1, x2) ∈ R2; 2x1+x2 ≥ 1} convex? Justify your objection.

A: Consider the set      S = {(x1, x2) ∈ R2 : 2x1 + x2 ≥ 1} Let, the points (x1, x2), (x3, x4) be in S.…

Q: Exercise. Consider the set R?. For every r = (x1, x2) E R? and y = (Yı, 42) E R², write P1(x, y) =|…

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Q: TOVE 4.55. Let A, B and C be sets. Prove that (A-B) (A-C)=A-(BUC).

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Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

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Q: 2) Explain how you count the number of elements in the set A = {n EN| n <500 and gcd (n, M) = 1},…

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Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

Q: In each of the questions below identify the statement that does not hold in a complete ordered field…

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

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: Q#6. Given any sets A and B define the symmetric difference of A and B (ΑΘΒ) -(Α-Β ) υ (B - Α) prove…

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Q: Determine whether the following sets are convex (1) {(x,y)=√x + √√]]l}

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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: P(0) = {0} P(A) \ {0} P(A) ACB iff P(A) CP(B).

A: According to guideline we need to solve first three question. Rest of the question should be…

Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

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Q: Prove that for the sets. B={4x+3|X€Z3 we have A =B

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