3. Let An, A, Bn, B be subsets of 2. Showlim sup A, U Bn = lim sup A, U lim sup Bn.n-00n00If A, → A and B, → B, is it true thatAn U Bn → AU B, Ann Bn→ AN B?1.9 Exercises214. SupposemAn = {-: m e N}, ne N,nwhere N are non-negative integers. What islim inf An and lim sup A,?n-00n-00

3) let An , A , Bn , B be the subsets of Ω show that limn→∞supAn∪Bn=limn→∞sup An ∪limn→∞supBn if…

Answered: 3. Let An, A, Bn, B be subsets of 2.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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show that ( A u B) ˄ ( ^B u C) -> ( A v C ) is a tautology
2. Let A = {1,2, 3}, B = {4, 5, 6}, C = {7,8, 9}. Consider the relations R from A to B, S from B to C, and T on A. R = {(1, 5), (2, 4), (1, 6)} S = {(4, 8), (5, 7), (6, 8), (6, 9)} Т 3 {(1,2), (2, 3), (3, 1), (1, 1), (2, 2), (3, 3)} Find the following relations (a) Find the compositions Ro S, T o R, T o T. (b) Find the matrices MR, Ms, MT, MTOT, MTOR and MRos of the respective relations R, S, т, То Т, То R, and Ro S.
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
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f S={1,2,3,4, 5,6,7, 8, 9}, A- {2,4,1,a}, 8-{1,3,5,7,a3. c:{2,04,53, and D-{1,6,73, list the elements the sets oF corresponding to the following cuents. 9:) A'UC b.) Bn c C)(s NB')
The difference of two sets, A – B, is defined as the set containing all elements of A except those in B. That is, A - B = AN B'. Find A - B for the pair of sets if U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. (Enter your answer in roster notation. Enter EMPTY or Ø for the empty set.) A = {3, 5, 9} and B = {2, 4, 6, 7, 8, 9} A - B =
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3. Let An, A, Bn, B be subsets of 2. Show lim sup A, U Bn = lim sup A, U lim sup Bn. n-00 n-00 If A, + A and Bn → B, is it true that A, U Bn → AU B, An N Bn → AN B?