1. Is the following axiom system consistent/dependent? a. There are six points. b. There are three 3-point lines. c. There are at least three 2-point lines. of a near-linear space

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

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Q: 39. Which of the following is not correct: O The product of two separable spaces is second countable…

A: First one is not correct.

Q: STRICLY NEED A DIAGRAM A. Given a certain system that has the following set of axioms: A1: There…

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Q: What topology does one get on the real line if one imposes both the left and right Sorgenfrey…

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Q: 12. Statement 1: All X are Y Statement 2: All Z are X Statement 3: Therefore, A. all Z are Y B. some…

A: Statement 1:All X are YStatement 2:All Z are XStatement 3: therefore=?

Q: 37. Which of these three statements is/are not true? I: Every finite nonempty subset of R has a…

A: We shall answer all the parts and provide justification as to why a particular part is not true. In…

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Q: Choose the response that correctly completes the following statements: • The graph of r = 4 in…

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Q: Proposition 1.43. A is the intersection of all closed subsets of X which con- tains A. Proof.…

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Q: 3 Let A = -6 -1 -2 and v = -6- -2 3 Av = -6 2 -9 Ex: 5 s v in null(A)? Select an option

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Q: Consider the set C = {x : Ax < b}, A e Rm×n and be R". Describe the set7 of feasible directions d at…

A: Given: The set C=x:Ax≤b, A∈ℝm×n and b∈ℝm   To describe: The set of feasible directions d at a point…

Q: 1. Suppose that we have the binary relations R1 C A× B, R2 C Bx C, and R3 C C x D. Then the…

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Q: Let a₁ = -3 h -2 a₂ = -6 1 , and a3 = -8 20 The set {a₁, a2, a3}| will span R³ unless h = 19 (If…

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Q: Let A= {k: k ∈ N, k ≤ 20}, B= {3k−1: k ∈ N}, and C= {2k+1: k ∈ N} 1. A INTERSECTION B INTERSECTION…

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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 ∅ be the empty set. Let X be the real line, the entire plane, or, in the three-dimensional case,…

A: Given:

Q: 2. Let A = [1,3], B = {5}, and C = [4,6]. Write the inequalities (or equalities) that specify each…

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Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

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}

Q: 4. Prove each of the following statements: a). If a,b,r € R and a² + b² ≤r², b). If S={(x,y) = R²…

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Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: This is a question with multiple sub-parts.So I solve only first three parts. Re-post the question…

Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: Let P(x; y) : x plays in y A(x) : x is athletic. S(x) : x is smart.  E(y) : y is in English…

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Q: (4) Let X and Y be sets. Select which one of the following statements is equivalent to the statement…

A: It is given that PX∪Y×Y⊆PX×X∪Y where X and Y are sets. Here P(X) denotes the power set of X. We know…

Q: True or False?

A:

Q: write true or false for each statement  1. {∅}⊆{∅,{∅}}   2. ∅⊈∅   3. {∅}∈{∅}

A: The answers are given below:

Q: 3. Let A, B, C be sets. Provide a proof or a counterexample for each of the following statements. a.…

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Q: Let A, B and C be sets. Consider the following statements. Which of them are true? 1. Ax B = B×A 2.…

A: Given that A, B and C are sets. Note: According to Bartleby guidelines we can solve only first three…

Q: (c) A \ B = A \ (An B). (d) A = (ANB) U (A \ B).

A:

Q: Suppose that U and V are finite sets with |U| = m and |V| = are the maximum and minimum possible…

A: Maximum and minimum values of the set

Q: Determine (with argument) whether the following subsets of R are sub- spaces: 1. {(a, b, c) E R³ | a…

A: By Bartleby guidelines I can only answer the first three sub-questions. please repost the question…

Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

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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:…

A: The given set S=212, 122, 334, 1-10. We have to check whether the set S is Linearly independent or…

Q: Prove that |x|−|y|≤|x − y|. Hint: Apply the triangle inequalityto y and x − y.

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Q: a Are ALL the following three pairs in the relation R: (4.2) (1,2) (5,1) b Is 4 a minimum element?…

A: R=4,21,2,5,1a. (1,2) is not the element of R because from Hass diagram 2 is related to 1    here…