question d e Determine whether each of the following is a closed set.(a) A = [2,3] U [4,7](b) B = (-∞, 2] U [3,5](c) C = R \(-1,1)(d) D= [1,2) U [2, 4](e) E = (1, 2) U (3, 4]

The given sets, d) D=[1, 2)∪2, 4. e) E=1, 2∪(3, 4]. We have to determine whether the set is a closed…

Answered: Determine whether each of the following…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 25E: Determine whether the set S={1,x2,2+x2} spans P2.

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Determine whether the set S={1,x2,2+x2} spans P2.
Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
Find all subsets of the set S={(1,3,2),(4,1,1),(2,7,3),(2,1,1)} that form a basis for R3.
(4) Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C) = (A × B) \ (A × C). Prove that (A x B) n (C x D) = (ANC) × (BND).
D=(1) what are the combinations of elements
Determine whether each of the following is a closed set. (a) A = [2,3] U [4,7] (b) B = (-∞, 2] U [3,5] (c) C = R \(-1,1) (d) D= [1,2) U [2, 4] (e) E = (1, 2) U (3, 4]
II. Let 2-set of all real numbers, A-index set. Identify the generalized union and intersection of the following: 1. A₁-[0,4], A2-[1,5), A- [0.5,3], A- (1,9] As-[-5,8) where A = {1,2,3,4,5) 2. A-[0,4], A2-[1,5), A- [0.5,3], A (1,9] As [-5,-2) where A = {1,2,3,4,5) 3. Ax= {2, 2+2, 2+4,2+6, 2+8} where A = {2,4,6,8} 4. Az =(1-22, 1+22) where A = Z* 5. Ax (0, 32, 62} where A = Z' = 6. A[5, 10-] where A = Z' 7. Ax (5+, 10+) where A = 1 = Z' = 8. A (5+. 10-) where A = Z' 9. Ax= [5+10-] where A = Z 10. A (1, 10) where A = = = (0,1)
(1.) Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Suppose five integers are chosen from T. Show that it is not true that there must be two integers whose sum is 10 by giving a counterexample. In other words, fill in the blank with five numbers from T, no two of which have a sum of 10. (Enter your answer in set-roster notation.) (2.) Suppose five pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why? Since there are 5 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be............? . It follows that if a minimum of............. boots is chosen, at least two must be from the same pair.
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Consider the relations R = {(1,5), (2, 2), (3, 4), (5, 2)}, S = {(2,4), (3, 4), (3, 1), (5, 5)}, T = {(1,4), (3, 5), (4, 1)} on the set A = {1,2,3, 4, 5}. Find (a) SoR = (b) RoT = (c) ToS = (d) Ro R= (e) SoS = (() ТоТ%—
. Tell whether the following sets are open: (Justify your answer.) (a) (3,5) U {6} (b) (-∞, 0) U (0, 1) (c) {1, 2, 3, 4, 5, 6, 7, 8, 9) (d) (-∞, 0) U[0, 1) (e) Z (f) (-∞,0) U (0, 1] (h) R - {1, 2, 3} (j) { //: neN} U {0} (1) Qn (0,1) (g) (-∞,0) U [0, 1] (i) { //:ne N} (k) Q
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Determine whether each of the following is a closed set. (a) A = [2,3] U [4,7] (b) B= (-∞, 2] U [3,5] (c) C = R \(-1, 1) (d) D= [1, 2) U [2, 4] (e) E = (1, 2) U (3, 4]