3. Prove that if Z₁ Z₂ Z3 = 0, then at least one of the three factors is zero. 4. Show that a set S is unbounded if and only if every neighborhood of the point at infinity contains at least one point in S.

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Q: 2. Prove that is real if and only if z = z. Z Y

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: Let A, B, and C be sets (a) Prove that ACB iff A – B = Ø. (b) Prove that if A C BUCand ANB = Ø, then…

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Q: a. Vitali Theorem

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Q: Prove that B = (0,1) is NOT a compact set.

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Q: 1. Find all regular points of the set : {x € Rª | 2(x1+x2+x3)³ +3(x1+x2+x3)² = 1, x²+x²+x²+x4 = 1}.

A: The given set is: x∈R4|2(x1+x2+x3)3+3(x1+x2+x3)3=1,x12+x22+x32+x4=1

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Q: Prove that if C is a point of −→AB other than A, then −→AC = −→AB.

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Q: 5. Consider the following statement: For all sets A, B, and C, then AU (BNC) = (AUB) nC. Either…

A: Let value of set A,set B and set C are respectively. A={1,2,3,6,7} B={3,7,8,9} C={2,3,6,9}

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Q: Claim 3. Let A and B be sets. Then A = B if both of the following condi- tions are satisfied: . АС…

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Q: Determine whether the given set is linearly independent.

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Q: Exercise 3.3.16. Prove or find a counterexample to the following statement. Let A, B and C be sets.…

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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: Let (pos S) be the set of all positive combinations of the points of S. Which of the following…

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Q: Find the null space for A. 12 0 [4] -3 -4 -1 6-6 9 A = null(A) = span 100

A: The given matrix is A=120-3-4-16-69 We have to find the null space of the given matrix.

Q: Let An denote the number of lattice paths from (0,0) to (n, n) that do not pass above the diagonal y…

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Q: Ex 12.8. Let S be a set of q + 2 points in a projective plane of order q. Prove that every line,…

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Q: Determine if the set S = {1+ – 2x2, 2 + 5x- a², a + a2 }is linearly independent or linearly…

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Q: Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: If a € R such that 0 0, then show that a = 0.

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Q: Show that both R and R² may be covered by countably many open balls.

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Q: A set L cR is convex if:

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Q: Which of the following statements is correct about the set S = 2 3 ··· 2 3 2 4 []}} ? 0 Select one:…

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Q: Prove that X and Y are independent if and only if R = 0

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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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