-5 h -25 Let aj = a, = and az = 5 5 The set {a1, a2, az } will span R' unless h =| (If there are no values of h that make the set fail to span, enter "NONE". If the set fails to span for all values of h enter "ALL".)

Q: 6. h -19 Let a1 = 8. a2 = and az -14 -2 -3 3 The set {a1, a2, az} will span R³ unless h =

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Q: Set roster notation of U={r € Z l -2<r<2

A: we have given the set U = {r∈Z,  -2&lt;r&lt;2} we have to write the set roster notation of U The set…

Q: 8. Consider the set S = {(x,y) E R²: a >0 and y 2 0}. (a) Explain your answers. Find dS, S° and…

A: I  have used definition for each terms

Q: 7. (Relations) Consider the set A = (1,2,3, 4, 5}, and a relation R defined by zRy + 2-y is an…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: Theorem: (i) If Fa is a closed set for each a er then Fa is closed. aer (ii) If Fk is a closed set…

A: 1. Let X be a metric space such that Fα ⊂X. Consider X-∩α∈τ Fα=X ∩∩α∈τ Fαc              [A-B=A∩Bc]…

Q: -8. a. Show that if A and B are independent, then P(A|B) = P(A). b. Say we have sets A, B, and C (do…

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Q: -3 Let m be a real number and M = -69 If M is a linearly dependent set of M22 then m=4 m=6 m=1 None…

A: Let , m be real number. We know that , M2,2 is a set of 2×2 matrices. We have given that ,  M =…

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} ar are %3D %3D two sets. find R = {(x, y): x EX and y EY…

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Q: 10 h Let aj = -15 a, = -13 and az = -7 -5 -5 The set {aj, a2, az } will span R' unlessh = (If there…

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Q: Properties of a Map Consider the following arrow diagram. Select all options true of this diagram. O…

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Q: -U- B Clay Huron Arbor Salem P Dover Flint Ozark Utica In a certain county, there is a passenger…

A: topic -sets

Q: 3. Let R and S be relations on a set A then (SoR)-1 = R-1o s-1.

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Q: X: a universe containing the sets A,B,C. Then (C∩B)∩A⊆A∪(X−B)

A: Given that the universal set X contains the three sets A,B and C. To prove: C∩B∩A⊆A∪X-B where,…

Q: Sets L and Jare defined as follows. L = {g,h, i, j, k} J = {i,l, m, n, o} || || Find the…

A: Given, sets L and J are defined as follows: L = {g,h,i,j,k} J = { i,l,m,n,o}

Q: 5. (10 points) Let N(S) denote the number of elenents of a set S. Comider the following information…

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Q: Q4. Let A = {6m + 1: m € Z} and B = {12n-5:n € Z} be subsets of a universal set U. a. Show that A &…

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Q: The subject is on Elements of Set Theory.I really need help and explanation.

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Q: Question: Prove or disprove the conjectures: (a) {x|3y€ R:x= y² – 2y} = R. (b) If A, B, C are sets,…

A: (a) Given that x|∃y∈R:x=y2-2y=R Consider some value of y belongs to R Therefore,…

Q: a+b Let w = b a,beR be a subset of R³. A set S such that W= span S a-3b is: Select one: O A. W =…

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Q: tor all l sets A, Bad C やok that A xCB-c) = (AX1B J- CAxc). %3D

A: Given below the detailed solution

Q: 7. A, B, and C are subsets of a set S. Prove the following set identities using the basic set…

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Q: (4) < sup(B). 6. For A, B C R, define A + B = {a+b: a E A, b E B} A-B = {a •b: a E A, b E B} (i)…

A: defined set A·B=a·b:a∈A,b∈B 6(iii) give an example of sets A,B where supA·B≠supA·supB

Q: True or False Label each of the following true or false:- AX B = B X A for all nonempty sets A and…

A: Let A=1 and B=2.Since, A×B=(a,b)|a∈A, b∈BTherefore, A×B={1,2} -(i)and also, B×A=(b,a)|b∈B,…

Q: 1 -2 -17 Let A: -3 3 and b = b2 Describe the set of all b for which Ax = b is consistent. 2 -1 1 b3

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Q: d. Universal set = {Students at CCD} R={Enrolled in a History Class} S={Enrolled in a English Class}…

A: First venn diagram will be answer.    Since there must be some student enrolled for only history,…

Q: |somotphic (Similar) orderede sets: suppose x anel y are partially ordered set ,and fixay…

A: We have to give the example of the isomorphic ordered set.

Q: 25 h 28 Let a1 = -25 az = 16 and az = -26 The set {a1, a2, az} will span R³ unless h = If there are…

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Q: {-5, –3, –1, 1, 3, 5}, Let A 3D {-5, —-4, —3, —2, —1,0, 1, 2, 3, 4, 5}, В D = {1,2, 3, 4}, E =…

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Q: 2. Let A = {0,1, 2, 4, 5, 7} and B = {2,3, 4, 5, 8} be subsets of the set %3D %3D U = {n € Z | 0 < n…

A: Given: A=0,1,2,4,5,7  &amp; B=2,3,4,5,8 is subset of U=n∈ℤ  0≤n≤9 i.e.U=0,1,2,3,4,5,6,7,8,9 To Find…

Q: Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the set:…

A: An upper bound of a set S is an element  which is greater than or equal to every element of S.The…

Q: Refer to the geometric figures below: Identify the finite geometries described by the following…

A: a. Consider the given figures, it can be observed that the diagram B has exactly 4 distinct points.…

Q: Topology: Give five pairs of things and words (3-, 4-, 5-letter words, respectively) that are…

A: We need to find, 5 pairs of things are homeomorphic. 5 pairs of words that are homeomorphic.

Q: Q 1 (a) Give an example of sets A and B such that (An B) # A°n B°. (b) Prove that for all sets A and…

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Q: 2. 1) Lot A = P(Ø), B = P([a,b}), and C = P({a,c}) where P(S) is the power %3D %3D set of S. Find…

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Q: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

Q: K*2K-1 show that the set u (2²2) is open K =) (Hint-Ch-Exercise and find its measure 1.53 3.]

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Q: 1. Prove DeMorgan's Laws. That is, let X be a set and let A and B be subsets of X. Show that (a) X –…

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Q: I. Let the universal set U= {0 < # < 20}. Let A = {1, 4, 7, 10, 19, 15, 14}. B = {1, 7, 19, 8, 5},…

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Q: I) We know that -5,-4,-3,-2,-1 and IN are well-ordered sets with respect to the trivial ordering.…

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Q: -20 Let a = 10 az = -11 and az = 5 -3 4 The set {a, a2, az } will span R³ unless h (If there are no…

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Q: 0.3: let X= R, A=[0,] and TA) = {0,4,x] Q.3. (3-Get topelogy) Q Frnd all the closed Sets inB, ICA))…

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Q: Challenge Problem. Let U be some universal set, and let S = {A e U | A ¢ A}. a. Show that S ¢ S. b.…

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Q: THEOREM 2.8 (DeMorgan's Laws). Let A, B, and C be sets. Then (a) A- (BnC) = (A – B)U (A - C), and…

A: Here we use venn diagram to prove DeMorgan's law

Q: The set A={x: xEN,x^2-3x+2 = 0} is %3D Null set Finite set Infinite set None of these

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Q: 1) We know that -5,-4 sets with respect to the trivial ordering. Let X=2-5,-4 -3,-2,-1U N.Prove that…

A: Trivially ordered set: A partially ordered set X in which distinct element are incomparable. x≤y⇔x=y…

Q: h and a2 6 Let aj -12 The set faj, a,} will span R unless h = (If there are no values of h that make…

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Q: I) We know that F-5,-4,-3,-2,-14 and N aire well-ordered sets with respect to the trivial ordering.…

A: Step:-1 Well ordering Principle:- An ordered set is said to be well ordered if each and every…

Q: 17–20 ■ Intervals Express the inequality in interval notation,and then graph the corresponding…

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Q: I) We know that {-5,-4,-3,-2,-14 and IN are well-orderec sets with respect to the trivial ordering.…

A: Given information :  -5, -4, -3, -2, -1 and ℕare well ordered sets with respect to trivial ordering.…

Q: The set of all triples of real numbers (x, y, z) with the operations x, y,2) + (x', y',z') = (x +…

A: Given : set of all triples of real numbers x, y, z with the operations   x, y, z+x', y', z'=x+x',…