Elementary Algebra: Concepts and Applications (10th Edition)
10th Edition
ISBN: 9780134441375
Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 8, Problem 8RE
To determine
Whether the statement, ‘The rule for adding or multiplying integer exponents also apply to rational exponents’ is true or false.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Use the graph to solve 3x2-3x-8=0
Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Chapter 8 Solutions
Elementary Algebra: Concepts and Applications (10th Edition)
Ch. 8.1 - Find the square roots of 81.Ch. 8.1 - Prob. 2YTCh. 8.1 - Prob. 3YTCh. 8.1 - Prob. 4YTCh. 8.1 - Prob. 5YTCh. 8.1 - Prob. 6YTCh. 8.1 - Prob. 7YTCh. 8.1 - Prob. 8YTCh. 8.1 - Prob. 1CYUCh. 8.1 - Prob. 2CYU
Ch. 8.1 - Prob. 3CYUCh. 8.1 - Prob. 4CYUCh. 8.1 - Prob. 5CYUCh. 8.1 - Prob. 6CYUCh. 8.1 - Prob. 7CYUCh. 8.1 - Prob. 8CYUCh. 8.1 - Prob. 1ESCh. 8.1 - Prob. 2ESCh. 8.1 - Prob. 3ESCh. 8.1 - Prob. 4ESCh. 8.1 - Prob. 5ESCh. 8.1 - Prob. 6ESCh. 8.1 - Prob. 7ESCh. 8.1 - Classify each of the following statements as...Ch. 8.1 - Prob. 9ESCh. 8.1 - Prob. 10ESCh. 8.1 - Prob. 11ESCh. 8.1 - Prob. 12ESCh. 8.1 - Prob. 13ESCh. 8.1 - Prob. 14ESCh. 8.1 - Prob. 15ESCh. 8.1 - Prob. 16ESCh. 8.1 - Prob. 17ESCh. 8.1 - Prob. 18ESCh. 8.1 - Prob. 19ESCh. 8.1 - Prob. 20ESCh. 8.1 - Prob. 21ESCh. 8.1 - Prob. 22ESCh. 8.1 - Prob. 23ESCh. 8.1 - Prob. 24ESCh. 8.1 - Prob. 25ESCh. 8.1 - Prob. 26ESCh. 8.1 - Prob. 27ESCh. 8.1 - Prob. 28ESCh. 8.1 - Prob. 29ESCh. 8.1 - Prob. 30ESCh. 8.1 - Prob. 31ESCh. 8.1 - Prob. 32ESCh. 8.1 - Prob. 33ESCh. 8.1 - Prob. 34ESCh. 8.1 - Prob. 35ESCh. 8.1 - Prob. 36ESCh. 8.1 - Prob. 37ESCh. 8.1 - Prob. 38ESCh. 8.1 - Prob. 39ESCh. 8.1 - Prob. 40ESCh. 8.1 - Prob. 41ESCh. 8.1 - Prob. 42ESCh. 8.1 - Prob. 43ESCh. 8.1 - Prob. 44ESCh. 8.1 - Prob. 45ESCh. 8.1 - Prob. 46ESCh. 8.1 - Prob. 47ESCh. 8.1 - Prob. 48ESCh. 8.1 - Prob. 49ESCh. 8.1 - Prob. 50ESCh. 8.1 - Prob. 51ESCh. 8.1 - Prob. 52ESCh. 8.1 - Prob. 53ESCh. 8.1 - Prob. 54ESCh. 8.1 - Prob. 55ESCh. 8.1 - Prob. 56ESCh. 8.1 - Prob. 57ESCh. 8.1 - Prob. 58ESCh. 8.1 - Prob. 59ESCh. 8.1 - Prob. 60ESCh. 8.1 - Prob. 61ESCh. 8.1 - Prob. 62ESCh. 8.1 - Prob. 63ESCh. 8.1 - Prob. 64ESCh. 8.1 - Prob. 65ESCh. 8.1 - Prob. 66ESCh. 8.1 - Prob. 67ESCh. 8.1 - Prob. 68ESCh. 8.1 - Prob. 69ESCh. 8.1 - Prob. 70ESCh. 8.1 - Hang Time. An athletes hang time (time airborne...Ch. 8.1 - Prob. 72ESCh. 8.1 - Prob. 73ESCh. 8.1 - Prob. 74ESCh. 8.1 - Prob. 75ESCh. 8.1 - Prob. 76ESCh. 8.1 - Prob. 77ESCh. 8.1 - Prob. 78ESCh. 8.1 - Prob. 79ESCh. 8.1 - Prob. 80ESCh. 8.1 - Prob. 81ESCh. 8.1 - Prob. 82ESCh. 8.1 - Prob. 83ESCh. 8.1 - Prob. 84ESCh. 8.1 - Prob. 85ESCh. 8.1 - Prob. 86ESCh. 8.1 - Prob. 87ESCh. 8.1 - Prob. 88ESCh. 8.1 - Prob. 89ESCh. 8.1 - Prob. 90ESCh. 8.1 - Prob. 91ESCh. 8.1 - Prob. 92ESCh. 8.1 - Prob. 93ESCh. 8.1 - Prob. 94ESCh. 8.1 - Prob. 95ESCh. 8.1 - Prob. 96ESCh. 8.1 - Prob. 97ESCh. 8.1 - Prob. 98ESCh. 8.1 - Prob. 99ESCh. 8.1 - Prob. 100ESCh. 8.1 - Prob. 101ESCh. 8.1 - Prob. 102ESCh. 8.1 - Prob. 103ESCh. 8.1 - Prob. 104ESCh. 8.1 - Prob. 105ESCh. 8.1 - Prob. 106ESCh. 8.1 - Prob. 107ESCh. 8.1 - Prob. 108ESCh. 8.1 - Prob. 1PTMOCh. 8.1 - Prob. 2PTMOCh. 8.1 - Prob. 3PTMOCh. 8.1 - Prob. 4PTMOCh. 8.1 - Prob. 5PTMOCh. 8.2 - Prob. 1YTCh. 8.2 - Prob. 2YTCh. 8.2 - Prob. 3YTCh. 8.2 - Prob. 4YTCh. 8.2 - Prob. 5YTCh. 8.2 - Prob. 6YTCh. 8.2 - Prob. 1CYUCh. 8.2 - Prob. 2CYUCh. 8.2 - Prob. 3CYUCh. 8.2 - Prob. 4CYUCh. 8.2 - Prob. 5CYUCh. 8.2 - Prob. 6CYUCh. 8.2 - Prob. 7CYUCh. 8.2 - Prob. 8CYUCh. 8.2 - Prob. 1ESCh. 8.2 - Prob. 2ESCh. 8.2 - Prob. 3ESCh. 8.2 - Prob. 4ESCh. 8.2 - Prob. 5ESCh. 8.2 - Prob. 6ESCh. 8.2 - Prob. 7ESCh. 8.2 - Prob. 8ESCh. 8.2 - Prob. 9ESCh. 8.2 - Prob. 10ESCh. 8.2 - Prob. 11ESCh. 8.2 - Prob. 12ESCh. 8.2 - Prob. 13ESCh. 8.2 - Prob. 14ESCh. 8.2 - Prob. 15ESCh. 8.2 - Prob. 16ESCh. 8.2 - Prob. 17ESCh. 8.2 - Prob. 18ESCh. 8.2 - Prob. 19ESCh. 8.2 - Prob. 20ESCh. 8.2 - Prob. 21ESCh. 8.2 - Prob. 22ESCh. 8.2 - Prob. 23ESCh. 8.2 - Prob. 24ESCh. 8.2 - Prob. 25ESCh. 8.2 - Prob. 26ESCh. 8.2 - Prob. 27ESCh. 8.2 - Prob. 28ESCh. 8.2 - Prob. 29ESCh. 8.2 - Prob. 30ESCh. 8.2 - Prob. 31ESCh. 8.2 - Prob. 32ESCh. 8.2 - Prob. 33ESCh. 8.2 - Prob. 34ESCh. 8.2 - Prob. 35ESCh. 8.2 - Prob. 36ESCh. 8.2 - Prob. 37ESCh. 8.2 - Prob. 38ESCh. 8.2 - Prob. 39ESCh. 8.2 - Prob. 40ESCh. 8.2 - Prob. 41ESCh. 8.2 - Prob. 42ESCh. 8.2 - Prob. 43ESCh. 8.2 - Prob. 44ESCh. 8.2 - Prob. 45ESCh. 8.2 - Prob. 46ESCh. 8.2 - Prob. 47ESCh. 8.2 - Prob. 48ESCh. 8.2 - Prob. 49ESCh. 8.2 - Prob. 50ESCh. 8.2 - Prob. 51ESCh. 8.2 - Prob. 52ESCh. 8.2 - Prob. 53ESCh. 8.2 - Prob. 54ESCh. 8.2 - Prob. 55ESCh. 8.2 - Prob. 56ESCh. 8.2 - Prob. 57ESCh. 8.2 - Prob. 58ESCh. 8.2 - Prob. 59ESCh. 8.2 - Prob. 60ESCh. 8.2 - Prob. 61ESCh. 8.2 - Prob. 62ESCh. 8.2 - Prob. 63ESCh. 8.2 - Prob. 64ESCh. 8.2 - Prob. 65ESCh. 8.2 - Prob. 66ESCh. 8.2 - Prob. 67ESCh. 8.2 - Prob. 68ESCh. 8.2 - Prob. 69ESCh. 8.2 - Prob. 70ESCh. 8.2 - Prob. 71ESCh. 8.2 - Prob. 72ESCh. 8.2 - Prob. 73ESCh. 8.2 - Prob. 74ESCh. 8.2 - Prob. 75ESCh. 8.2 - Prob. 76ESCh. 8.2 - Prob. 77ESCh. 8.2 - Prob. 78ESCh. 8.2 - Prob. 79ESCh. 8.2 - Prob. 80ESCh. 8.2 - Prob. 81ESCh. 8.2 - Prob. 82ESCh. 8.2 - Prob. 83ESCh. 8.2 - Prob. 84ESCh. 8.2 - Prob. 85ESCh. 8.2 - Prob. 86ESCh. 8.2 - Prob. 87ESCh. 8.2 - Prob. 88ESCh. 8.2 - Prob. 89ESCh. 8.2 - Prob. 90ESCh. 8.2 - Prob. 91ESCh. 8.2 - Prob. 92ESCh. 8.2 - Prob. 93ESCh. 8.2 - Prob. 94ESCh. 8.2 - Prob. 95ESCh. 8.2 - Explain why the rules for manipulating exponents...Ch. 8.2 - Prob. 97ESCh. 8.2 - Prob. 98ESCh. 8.2 - Prob. 99ESCh. 8.2 - Prob. 100ESCh. 8.2 - Prob. 101ESCh. 8.2 - Prob. 102ESCh. 8.2 - Prob. 103ESCh. 8.2 - Prob. 104ESCh. 8.2 - Prob. 105ESCh. 8.2 - Prob. 106ESCh. 8.2 - Prob. 107ESCh. 8.2 - Prob. 108ESCh. 8.2 - Prob. 109ESCh. 8.2 - Prob. 110ESCh. 8.2 - Prob. 111ESCh. 8.2 - Prob. 112ESCh. 8.2 - Prob. 113ESCh. 8.2 - Prob. 114ESCh. 8.2 - Prob. 115ESCh. 8.2 - Prob. 116ESCh. 8.2 - Prob. 117ESCh. 8.2 - Prob. 118ESCh. 8.2 - Prob. 119ESCh. 8.2 - Prob. 120ESCh. 8.2 - Prob. 121ESCh. 8.2 - Prob. 122ESCh. 8.2 - Prob. 123ESCh. 8.2 - Prob. 124ESCh. 8.2 - Prob. 1QQCh. 8.2 - Prob. 2QQCh. 8.2 - Prob. 3QQCh. 8.2 - Prob. 4QQCh. 8.2 - Prob. 5QQCh. 8.2 - Prob. 1PTMOCh. 8.2 - Prob. 2PTMOCh. 8.2 - Prob. 3PTMOCh. 8.2 - Prob. 4PTMOCh. 8.2 - Prob. 5PTMOCh. 8.3 - Prob. 1YTCh. 8.3 - Prob. 2YTCh. 8.3 - Prob. 3YTCh. 8.3 - Prob. 4YTCh. 8.3 - Prob. 5YTCh. 8.3 - Prob. 1CYUCh. 8.3 - Prob. 2CYUCh. 8.3 - Prob. 3CYUCh. 8.3 - Prob. 4CYUCh. 8.3 - Prob. 5CYUCh. 8.3 - Prob. 1ESCh. 8.3 - Prob. 2ESCh. 8.3 - Prob. 3ESCh. 8.3 - Prob. 4ESCh. 8.3 - Prob. 5ESCh. 8.3 - Prob. 6ESCh. 8.3 - Prob. 7ESCh. 8.3 - Prob. 8ESCh. 8.3 - Prob. 9ESCh. 8.3 - Prob. 10ESCh. 8.3 - Prob. 11ESCh. 8.3 - Prob. 12ESCh. 8.3 - Prob. 13ESCh. 8.3 - Prob. 14ESCh. 8.3 - Prob. 15ESCh. 8.3 - Prob. 16ESCh. 8.3 - Prob. 17ESCh. 8.3 - Prob. 18ESCh. 8.3 - Prob. 19ESCh. 8.3 - Prob. 20ESCh. 8.3 - Prob. 21ESCh. 8.3 - Prob. 22ESCh. 8.3 - Prob. 23ESCh. 8.3 - Prob. 24ESCh. 8.3 - Prob. 25ESCh. 8.3 - Prob. 26ESCh. 8.3 - Prob. 27ESCh. 8.3 - Prob. 28ESCh. 8.3 - Prob. 29ESCh. 8.3 - Prob. 30ESCh. 8.3 - Prob. 31ESCh. 8.3 - Prob. 32ESCh. 8.3 - Prob. 33ESCh. 8.3 - Prob. 34ESCh. 8.3 - Prob. 35ESCh. 8.3 - Prob. 36ESCh. 8.3 - Prob. 37ESCh. 8.3 - Prob. 38ESCh. 8.3 - Prob. 39ESCh. 8.3 - Prob. 40ESCh. 8.3 - Prob. 41ESCh. 8.3 - Prob. 42ESCh. 8.3 - Prob. 43ESCh. 8.3 - Prob. 44ESCh. 8.3 - Prob. 45ESCh. 8.3 - Prob. 46ESCh. 8.3 - Prob. 47ESCh. 8.3 - Prob. 48ESCh. 8.3 - Prob. 49ESCh. 8.3 - Prob. 50ESCh. 8.3 - Prob. 51ESCh. 8.3 - Prob. 52ESCh. 8.3 - Prob. 53ESCh. 8.3 - Prob. 54ESCh. 8.3 - Prob. 55ESCh. 8.3 - Prob. 56ESCh. 8.3 - Prob. 57ESCh. 8.3 - Prob. 58ESCh. 8.3 - Prob. 59ESCh. 8.3 - Prob. 60ESCh. 8.3 - Prob. 61ESCh. 8.3 - Prob. 62ESCh. 8.3 - Prob. 63ESCh. 8.3 - Prob. 64ESCh. 8.3 - Prob. 65ESCh. 8.3 - Prob. 66ESCh. 8.3 - Prob. 67ESCh. 8.3 - Prob. 68ESCh. 8.3 - Prob. 69ESCh. 8.3 - Prob. 70ESCh. 8.3 - Prob. 71ESCh. 8.3 - Prob. 72ESCh. 8.3 - Prob. 73ESCh. 8.3 - Prob. 74ESCh. 8.3 - Prob. 75ESCh. 8.3 - Prob. 76ESCh. 8.3 - Prob. 77ESCh. 8.3 - Prob. 78ESCh. 8.3 - Prob. 79ESCh. 8.3 - Prob. 80ESCh. 8.3 - Prob. 81ESCh. 8.3 - Prob. 82ESCh. 8.3 - Prob. 83ESCh. 8.3 - Prob. 84ESCh. 8.3 - Prob. 85ESCh. 8.3 - Prob. 86ESCh. 8.3 - Prob. 87ESCh. 8.3 - Prob. 88ESCh. 8.3 - Prob. 89ESCh. 8.3 - Prob. 1QQCh. 8.3 - Prob. 2QQCh. 8.3 - Prob. 3QQCh. 8.3 - Prob. 4QQCh. 8.3 - Prob. 5QQCh. 8.3 - Prob. 1PTMOCh. 8.3 - Prob. 2PTMOCh. 8.3 - Prob. 3PTMOCh. 8.3 - Prob. 4PTMOCh. 8.3 - Prob. 5PTMOCh. 8.4 - Prob. 1YTCh. 8.4 - Prob. 2YTCh. 8.4 - Prob. 3YTCh. 8.4 - Prob. 4YTCh. 8.4 - Prob. 1CYUCh. 8.4 - Prob. 2CYUCh. 8.4 - Prob. 3CYUCh. 8.4 - Prob. 4CYUCh. 8.4 - Prob. 5CYUCh. 8.4 - Prob. 6CYUCh. 8.4 - Prob. 7CYUCh. 8.4 - Prob. 1TCCh. 8.4 - Prob. 2TCCh. 8.4 - Prob. 3TCCh. 8.4 - Prob. 4TCCh. 8.4 - Prob. 1ESCh. 8.4 - Prob. 2ESCh. 8.4 - Prob. 3ESCh. 8.4 - Prob. 4ESCh. 8.4 - Prob. 5ESCh. 8.4 - Prob. 6ESCh. 8.4 - Prob. 7ESCh. 8.4 - Prob. 8ESCh. 8.4 - Prob. 9ESCh. 8.4 - Prob. 10ESCh. 8.4 - Prob. 11ESCh. 8.4 - Prob. 12ESCh. 8.4 - Prob. 13ESCh. 8.4 - Prob. 14ESCh. 8.4 - Prob. 15ESCh. 8.4 - Prob. 16ESCh. 8.4 - Prob. 17ESCh. 8.4 - Prob. 18ESCh. 8.4 - Prob. 19ESCh. 8.4 - Prob. 20ESCh. 8.4 - Prob. 21ESCh. 8.4 - Prob. 22ESCh. 8.4 - Prob. 23ESCh. 8.4 - Prob. 24ESCh. 8.4 - Prob. 25ESCh. 8.4 - Prob. 26ESCh. 8.4 - Prob. 27ESCh. 8.4 - Prob. 28ESCh. 8.4 - Prob. 29ESCh. 8.4 - Prob. 30ESCh. 8.4 - Prob. 31ESCh. 8.4 - Prob. 32ESCh. 8.4 - Prob. 33ESCh. 8.4 - Prob. 34ESCh. 8.4 - Prob. 35ESCh. 8.4 - Prob. 36ESCh. 8.4 - Prob. 37ESCh. 8.4 - Prob. 38ESCh. 8.4 - Prob. 39ESCh. 8.4 - Prob. 40ESCh. 8.4 - Prob. 41ESCh. 8.4 - Prob. 42ESCh. 8.4 - Prob. 43ESCh. 8.4 - Prob. 44ESCh. 8.4 - Prob. 45ESCh. 8.4 - Prob. 46ESCh. 8.4 - Prob. 47ESCh. 8.4 - Prob. 48ESCh. 8.4 - Prob. 49ESCh. 8.4 - Prob. 50ESCh. 8.4 - Prob. 51ESCh. 8.4 - Prob. 52ESCh. 8.4 - Prob. 53ESCh. 8.4 - Prob. 54ESCh. 8.4 - Prob. 55ESCh. 8.4 - Prob. 56ESCh. 8.4 - Prob. 57ESCh. 8.4 - Prob. 58ESCh. 8.4 - Prob. 59ESCh. 8.4 - Prob. 60ESCh. 8.4 - Prob. 61ESCh. 8.4 - Prob. 62ESCh. 8.4 - Prob. 63ESCh. 8.4 - Prob. 64ESCh. 8.4 - Prob. 65ESCh. 8.4 - Prob. 66ESCh. 8.4 - Prob. 67ESCh. 8.4 - Prob. 68ESCh. 8.4 - Prob. 69ESCh. 8.4 - Prob. 70ESCh. 8.4 - Prob. 71ESCh. 8.4 - Prob. 72ESCh. 8.4 - Prob. 73ESCh. 8.4 - Prob. 74ESCh. 8.4 - Prob. 75ESCh. 8.4 - Prob. 76ESCh. 8.4 - Prob. 77ESCh. 8.4 - Prob. 78ESCh. 8.4 - Prob. 79ESCh. 8.4 - Prob. 80ESCh. 8.4 - Prob. 81ESCh. 8.4 - Prob. 82ESCh. 8.4 - Prob. 83ESCh. 8.4 - Prob. 84ESCh. 8.4 - Prob. 85ESCh. 8.4 - Prob. 86ESCh. 8.4 - Prob. 87ESCh. 8.4 - Prob. 88ESCh. 8.4 - Prob. 89ESCh. 8.4 - Prob. 90ESCh. 8.4 - Prob. 91ESCh. 8.4 - Prob. 92ESCh. 8.4 - Prob. 93ESCh. 8.4 - Prob. 1QQCh. 8.4 - Prob. 2QQCh. 8.4 - Prob. 3QQCh. 8.4 - Prob. 4QQCh. 8.4 - Prob. 5QQCh. 8.4 - Prob. 1PTMOCh. 8.4 - Prob. 2PTMOCh. 8.4 - Prob. 3PTMOCh. 8.4 - Prob. 4PTMOCh. 8.4 - Prob. 5PTMOCh. 8.4 - Prob. 1MCRCh. 8.4 - Prob. 2MCRCh. 8.4 - Prob. 3MCRCh. 8.4 - Prob. 4MCRCh. 8.4 - Prob. 5MCRCh. 8.4 - Prob. 6MCRCh. 8.4 - Prob. 7MCRCh. 8.4 - Prob. 8MCRCh. 8.4 - Prob. 9MCRCh. 8.4 - Prob. 10MCRCh. 8.4 - Prob. 11MCRCh. 8.4 - Prob. 12MCRCh. 8.4 - Prob. 13MCRCh. 8.4 - Prob. 14MCRCh. 8.4 - Prob. 15MCRCh. 8.4 - Prob. 16MCRCh. 8.4 - Prob. 17MCRCh. 8.4 - Prob. 18MCRCh. 8.4 - Prob. 19MCRCh. 8.4 - Prob. 20MCRCh. 8.5 - Prob. 1YTCh. 8.5 - Prob. 2YTCh. 8.5 - Prob. 3YTCh. 8.5 - Prob. 4YTCh. 8.5 - Prob. 1CYUCh. 8.5 - Prob. 2CYUCh. 8.5 - Prob. 3CYUCh. 8.5 - Prob. 4CYUCh. 8.5 - Prob. 5CYUCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 1ESCh. 8.5 - Prob. 2ESCh. 8.5 - Prob. 3ESCh. 8.5 - Prob. 4ESCh. 8.5 - Prob. 5ESCh. 8.5 - Prob. 6ESCh. 8.5 - Prob. 7ESCh. 8.5 - Prob. 8ESCh. 8.5 - Prob. 9ESCh. 8.5 - Prob. 10ESCh. 8.5 - Prob. 11ESCh. 8.5 - Prob. 12ESCh. 8.5 - Prob. 13ESCh. 8.5 - Prob. 14ESCh. 8.5 - Prob. 15ESCh. 8.5 - Prob. 16ESCh. 8.5 - Prob. 17ESCh. 8.5 - Prob. 18ESCh. 8.5 - Prob. 19ESCh. 8.5 - Prob. 20ESCh. 8.5 - Prob. 21ESCh. 8.5 - Prob. 22ESCh. 8.5 - Prob. 23ESCh. 8.5 - Prob. 24ESCh. 8.5 - Prob. 25ESCh. 8.5 - Prob. 26ESCh. 8.5 - Prob. 27ESCh. 8.5 - Prob. 28ESCh. 8.5 - Prob. 29ESCh. 8.5 - Prob. 30ESCh. 8.5 - Prob. 31ESCh. 8.5 - Prob. 32ESCh. 8.5 - Prob. 33ESCh. 8.5 - Prob. 34ESCh. 8.5 - Prob. 35ESCh. 8.5 - Prob. 36ESCh. 8.5 - Prob. 37ESCh. 8.5 - Prob. 38ESCh. 8.5 - Prob. 39ESCh. 8.5 - Prob. 40ESCh. 8.5 - Prob. 41ESCh. 8.5 - Prob. 42ESCh. 8.5 - Prob. 43ESCh. 8.5 - Prob. 44ESCh. 8.5 - Prob. 45ESCh. 8.5 - Prob. 46ESCh. 8.5 - Prob. 47ESCh. 8.5 - Prob. 48ESCh. 8.5 - Prob. 49ESCh. 8.5 - Prob. 50ESCh. 8.5 - Prob. 51ESCh. 8.5 - Prob. 52ESCh. 8.5 - Prob. 53ESCh. 8.5 - Prob. 54ESCh. 8.5 - Prob. 55ESCh. 8.5 - Prob. 56ESCh. 8.5 - Prob. 57ESCh. 8.5 - Prob. 58ESCh. 8.5 - Prob. 59ESCh. 8.5 - Prob. 60ESCh. 8.5 - Prob. 61ESCh. 8.5 - Prob. 62ESCh. 8.5 - Prob. 63ESCh. 8.5 - Prob. 64ESCh. 8.5 - Prob. 65ESCh. 8.5 - Prob. 66ESCh. 8.5 - Prob. 67ESCh. 8.5 - Prob. 68ESCh. 8.5 - Prob. 69ESCh. 8.5 - Prob. 70ESCh. 8.5 - Prob. 71ESCh. 8.5 - Prob. 72ESCh. 8.5 - Prob. 73ESCh. 8.5 - Prob. 74ESCh. 8.5 - Prob. 75ESCh. 8.5 - Prob. 76ESCh. 8.5 - Prob. 77ESCh. 8.5 - Prob. 78ESCh. 8.5 - Prob. 79ESCh. 8.5 - Prob. 80ESCh. 8.5 - Prob. 81ESCh. 8.5 - Prob. 82ESCh. 8.5 - Prob. 1QQCh. 8.5 - Prob. 2QQCh. 8.5 - Prob. 3QQCh. 8.5 - Prob. 4QQCh. 8.5 - Solve: 1+2x+3=6.[8.5]Ch. 8.5 - Prob. 1PTMOCh. 8.5 - Prob. 2PTMOCh. 8.5 - Prob. 3PTMOCh. 8.5 - Prob. 4PTMOCh. 8.5 - Simplify. [1.8]
5.
Ch. 8.6 - A right triangle has legs of lengths 3 and 10....Ch. 8.6 - Prob. 2YTCh. 8.6 - Prob. 3YTCh. 8.6 - Prob. 4YTCh. 8.6 - Prob. 5YTCh. 8.6 - Prob. 1CYUCh. 8.6 - Prob. 2CYUCh. 8.6 - Prob. 1ESCh. 8.6 - Prob. 2ESCh. 8.6 - Prob. 3ESCh. 8.6 - Prob. 4ESCh. 8.6 - Prob. 5ESCh. 8.6 - Prob. 6ESCh. 8.6 - Prob. 7ESCh. 8.6 - Prob. 8ESCh. 8.6 - Prob. 9ESCh. 8.6 - Prob. 10ESCh. 8.6 - Prob. 11ESCh. 8.6 - Prob. 12ESCh. 8.6 - Prob. 13ESCh. 8.6 - Prob. 14ESCh. 8.6 - Prob. 15ESCh. 8.6 - Prob. 16ESCh. 8.6 - Prob. 17ESCh. 8.6 - Prob. 18ESCh. 8.6 - Prob. 19ESCh. 8.6 - Prob. 20ESCh. 8.6 - Prob. 21ESCh. 8.6 - Prob. 22ESCh. 8.6 - Prob. 23ESCh. 8.6 - Prob. 24ESCh. 8.6 - Prob. 25ESCh. 8.6 - Prob. 26ESCh. 8.6 - Prob. 27ESCh. 8.6 - Prob. 28ESCh. 8.6 - Prob. 29ESCh. 8.6 - Prob. 30ESCh. 8.6 - Prob. 31ESCh. 8.6 - Prob. 32ESCh. 8.6 - 33. Reptiles. A snake’s cage should be large...Ch. 8.6 - Prob. 34ESCh. 8.6 - Prob. 35ESCh. 8.6 - Prob. 36ESCh. 8.6 - Prob. 37ESCh. 8.6 - Prob. 38ESCh. 8.6 - Prob. 39ESCh. 8.6 - Prob. 40ESCh. 8.6 - Prob. 41ESCh. 8.6 - Prob. 42ESCh. 8.6 - Prob. 43ESCh. 8.6 - Prob. 44ESCh. 8.6 - Prob. 45ESCh. 8.6 - Prob. 46ESCh. 8.6 - Prob. 47ESCh. 8.6 - Prob. 48ESCh. 8.6 - Prob. 49ESCh. 8.6 - Prob. 50ESCh. 8.6 - Prob. 51ESCh. 8.6 - Prob. 52ESCh. 8.6 - Prob. 53ESCh. 8.6 - Prob. 54ESCh. 8.6 - Prob. 55ESCh. 8.6 - Prob. 56ESCh. 8.6 - Prob. 57ESCh. 8.6 - Prob. 58ESCh. 8.6 - Prob. 59ESCh. 8.6 - Prob. 60ESCh. 8.6 - Prob. 61ESCh. 8.6 - Prob. 62ESCh. 8.6 - Prob. 63ESCh. 8.6 - Prob. 64ESCh. 8.6 - Prob. 65ESCh. 8.6 - Prob. 66ESCh. 8.6 - Prob. 67ESCh. 8.6 - Prob. 68ESCh. 8.6 - Prob. 69ESCh. 8.6 - Prob. 70ESCh. 8.6 - Prob. 1QQCh. 8.6 - Prob. 2QQCh. 8.6 - Prob. 3QQCh. 8.6 - Prob. 4QQCh. 8.6 - For Exercises 1-3, assume that all variables...Ch. 8.6 - Prob. 1PTMOCh. 8.6 - Prob. 2PTMOCh. 8.6 - Prob. 3PTMOCh. 8.6 - Prob. 4PTMOCh. 8.6 - Prob. 5PTMOCh. 8.7 - Prob. 1YTCh. 8.7 - Prob. 2YTCh. 8.7 - Prob. 3YTCh. 8.7 - Prob. 4YTCh. 8.7 - Prob. 5YTCh. 8.7 - Prob. 6YTCh. 8.7 - Prob. 1CYUCh. 8.7 - Prob. 2CYUCh. 8.7 - Prob. 3CYUCh. 8.7 - Prob. 4CYUCh. 8.7 - Prob. 5CYUCh. 8.7 - Prob. 1ESCh. 8.7 - Prob. 2ESCh. 8.7 - Prob. 3ESCh. 8.7 - Prob. 4ESCh. 8.7 - Prob. 5ESCh. 8.7 - Prob. 6ESCh. 8.7 - Prob. 7ESCh. 8.7 - Prob. 8ESCh. 8.7 - Prob. 9ESCh. 8.7 - Prob. 10ESCh. 8.7 - Prob. 11ESCh. 8.7 - Prob. 12ESCh. 8.7 - Prob. 13ESCh. 8.7 - Prob. 14ESCh. 8.7 - Prob. 15ESCh. 8.7 - Prob. 16ESCh. 8.7 - Prob. 17ESCh. 8.7 - Prob. 18ESCh. 8.7 - Prob. 19ESCh. 8.7 - Prob. 20ESCh. 8.7 - Prob. 21ESCh. 8.7 - Prob. 22ESCh. 8.7 - Prob. 23ESCh. 8.7 - Prob. 24ESCh. 8.7 - Prob. 25ESCh. 8.7 - Prob. 26ESCh. 8.7 - Prob. 27ESCh. 8.7 - Prob. 28ESCh. 8.7 - Prob. 29ESCh. 8.7 - Prob. 30ESCh. 8.7 - Prob. 31ESCh. 8.7 - Prob. 32ESCh. 8.7 - Prob. 33ESCh. 8.7 - Prob. 34ESCh. 8.7 - Prob. 35ESCh. 8.7 - Prob. 36ESCh. 8.7 - Prob. 37ESCh. 8.7 - Prob. 38ESCh. 8.7 - Prob. 39ESCh. 8.7 - Prob. 40ESCh. 8.7 - Prob. 41ESCh. 8.7 - Prob. 42ESCh. 8.7 - Prob. 43ESCh. 8.7 - Prob. 44ESCh. 8.7 - Prob. 45ESCh. 8.7 - Prob. 46ESCh. 8.7 - Prob. 47ESCh. 8.7 - Prob. 48ESCh. 8.7 - Prob. 49ESCh. 8.7 - Prob. 50ESCh. 8.7 - Prob. 51ESCh. 8.7 - Prob. 52ESCh. 8.7 - Prob. 53ESCh. 8.7 - Prob. 54ESCh. 8.7 - Prob. 55ESCh. 8.7 - Prob. 56ESCh. 8.7 - Prob. 57ESCh. 8.7 - Prob. 58ESCh. 8.7 - Prob. 59ESCh. 8.7 - Prob. 60ESCh. 8.7 - Prob. 61ESCh. 8.7 - Prob. 62ESCh. 8.7 - Prob. 63ESCh. 8.7 - Prob. 64ESCh. 8.7 - Prob. 65ESCh. 8.7 - Prob. 66ESCh. 8.7 - Prob. 67ESCh. 8.7 - Prob. 68ESCh. 8.7 - Prob. 69ESCh. 8.7 - Prob. 70ESCh. 8.7 - Prob. 71ESCh. 8.7 - Prob. 72ESCh. 8.7 - Prob. 73ESCh. 8.7 - Prob. 74ESCh. 8.7 - Prob. 75ESCh. 8.7 - Prob. 76ESCh. 8.7 - Prob. 77ESCh. 8.7 - Prob. 78ESCh. 8.7 - Prob. 79ESCh. 8.7 - Prob. 80ESCh. 8.7 - Prob. 81ESCh. 8.7 - Prob. 82ESCh. 8.7 - Prob. 83ESCh. 8.7 - Prob. 84ESCh. 8.7 - Prob. 85ESCh. 8.7 - Prob. 86ESCh. 8.7 - Prob. 87ESCh. 8.7 - Prob. 88ESCh. 8.7 - Prob. 1QQCh. 8.7 - Prob. 2QQCh. 8.7 - Prob. 3QQCh. 8.7 - Prob. 4QQCh. 8.7 - Prob. 5QQCh. 8.7 - Prob. 1PTMOCh. 8.7 - Prob. 2PTMOCh. 8.7 - Prob. 3PTMOCh. 8.7 - Prob. 4PTMOCh. 8.7 - Prob. 5PTMOCh. 8 - Prob. 1RVSCh. 8 - Prob. 2RVSCh. 8 - Prob. 3RVSCh. 8 - Prob. 4RVSCh. 8 - Prob. 5RVSCh. 8 - Prob. 6RVSCh. 8 - Prob. 7RVSCh. 8 - Prob. 8RVSCh. 8 - Prob. 9RVSCh. 8 - Prob. 10RVSCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Prob. 69RECh. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - Prob. 7TCh. 8 - Prob. 8TCh. 8 - Prob. 9TCh. 8 - Prob. 10TCh. 8 - Prob. 11TCh. 8 - Prob. 12TCh. 8 - Prob. 13TCh. 8 - Prob. 14TCh. 8 - Prob. 15TCh. 8 - Prob. 16TCh. 8 - Prob. 17TCh. 8 - Prob. 18TCh. 8 - Prob. 19TCh. 8 - Prob. 20TCh. 8 - Prob. 21TCh. 8 - Prob. 22TCh. 8 - Prob. 23TCh. 8 - Prob. 24TCh. 8 - Prob. 25TCh. 8 - Prob. 26TCh. 8 - Prob. 27TCh. 8 - Prob. 28TCh. 8 - Prob. 29TCh. 8 - Prob. 30TCh. 8 - Prob. 31TCh. 8 - Prob. 32TCh. 8 - Prob. 33TCh. 8 - Prob. 34TCh. 8 - Prob. 35TCh. 8 - Prob. 36TCh. 8 - Prob. 37TCh. 8 - Prob. 38TCh. 8 - Prob. 39TCh. 8 - Prob. 40TCh. 8 - Prob. 41TCh. 8 - Prob. 42TCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 14CRCh. 8 - Prob. 15CRCh. 8 - Prob. 16CRCh. 8 - Prob. 17CRCh. 8 - Prob. 18CRCh. 8 - Prob. 19CRCh. 8 - Prob. 20CRCh. 8 - Prob. 21CRCh. 8 - Prob. 22CRCh. 8 - Prob. 23CRCh. 8 - Prob. 24CRCh. 8 - Prob. 25CRCh. 8 - Prob. 26CRCh. 8 - Prob. 27CRCh. 8 - Prob. 28CRCh. 8 - Prob. 29CRCh. 8 - Prob. 30CRCh. 8 - Prob. 31CRCh. 8 - Prob. 32CRCh. 8 - Prob. 33CRCh. 8 - Prob. 34CRCh. 8 - Prob. 35CRCh. 8 - Prob. 36CRCh. 8 - Prob. 37CRCh. 8 - Prob. 38CRCh. 8 - Prob. 39CRCh. 8 - Prob. 40CRCh. 8 - Prob. 41CRCh. 8 - Prob. 42CRCh. 8 - Prob. 43CRCh. 8 - Prob. 44CRCh. 8 - Prob. 45CRCh. 8 - Prob. 46CRCh. 8 - Prob. 47CRCh. 8 - Prob. 48CRCh. 8 - Prob. 49CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]arrow_forwardR denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forward
- part b pleasearrow_forwardQuestion 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4arrow_forwardQuestion 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forward
- Tools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. Xarrow_forwardSimplify the below expression. 3 - (-7)arrow_forward(6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.arrow_forward
- 1. If f(x² + 1) = x + 5x² + 3, what is f(x² - 1)?arrow_forward2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forwardموضوع الدرس Prove that Determine the following groups Homz(QZ) Hom = (Q13,Z) Homz(Q), Hom/z/nZ, Qt for neN- (2) Every factor group of adivisible group is divisble. • If R is a Skew ficald (aring with identity and each non Zero element is invertible then every R-module is free.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY