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6. Let A = {x |x is a real number and 0

6. Let A = {x |x is a real number and 0

Advanced Engineering Mathematics
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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6. Let A = {x |x is a real number and 0 <x < 1}, B = {x |x is a real number and x? +1= 0}, C = {x | x = 4m, m e Z}, D = {0, 2, 4, 6 ...}, and E = (x |x € Z and x² < 100}. (a) Identify the following as true or false. %3D (i) CCD (iii) (4, 16} C E (ii) {4, 16} CC (iv) DCD (v) BCØ (b) Identify the following as true or false. (i) CNE¢ (CUE) (ii) øC (ANB) (iv) CUECD (iii) CND= D (v) ANDCANC 7. Let A = {x | x = 2n, n € Z*). B = {x |x = 2n + 1, n € Z*), C = {x |x = 4n, n € Z*), and D = {x | x(r² – 6x +8) = 0, x e Z}. Use Z as the universal set and find (a) AUB (b) Ā (c) (AN D) ® (AN B) (d) AUC (е) А- С 8. Draw a Venn diagram to represent (a) ANB and (b) ĀnB.
Transcribed Image Text:6. Let A = {x |x is a real number and 0 <x < 1}, B = {x |x is a real number and x? +1= 0}, C = {x | x = 4m, m e Z}, D = {0, 2, 4, 6 ...}, and E = (x |x € Z and x² < 100}. (a) Identify the following as true or false. %3D (i) CCD (iii) (4, 16} C E (ii) {4, 16} CC (iv) DCD (v) BCØ (b) Identify the following as true or false. (i) CNE¢ (CUE) (ii) øC (ANB) (iv) CUECD (iii) CND= D (v) ANDCANC 7. Let A = {x | x = 2n, n € Z*). B = {x |x = 2n + 1, n € Z*), C = {x |x = 4n, n € Z*), and D = {x | x(r² – 6x +8) = 0, x e Z}. Use Z as the universal set and find (a) AUB (b) Ā (c) (AN D) ® (AN B) (d) AUC (е) А- С 8. Draw a Venn diagram to represent (a) ANB and (b) ĀnB.
9. Under what conditions will ANB = AUB? 0. Suppose that 109 of the 150 mathematics students at Verysmall College take at least one of the following com- puter languages: PASCAL, BASIC, C++. Suppose 45 study BASIC, 61 study RASCAL, 53 study C++, 18 study BASIC and PASCAL, 15 study BASIC and C+*, and 23 study PASCAL and C++. (a) How many students study all three languages? (b) How many students study only BASIC? (c) How many students do not study any of the lan- guages? 1. Define a sequence as follows: ao = 0, a = 0, a, = 1- 3a-1 + 2a,-2. Compute the first six terms of this sequence.
Transcribed Image Text:9. Under what conditions will ANB = AUB? 0. Suppose that 109 of the 150 mathematics students at Verysmall College take at least one of the following com- puter languages: PASCAL, BASIC, C++. Suppose 45 study BASIC, 61 study RASCAL, 53 study C++, 18 study BASIC and PASCAL, 15 study BASIC and C+*, and 23 study PASCAL and C++. (a) How many students study all three languages? (b) How many students study only BASIC? (c) How many students do not study any of the lan- guages? 1. Define a sequence as follows: ao = 0, a = 0, a, = 1- 3a-1 + 2a,-2. Compute the first six terms of this sequence.
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