Identities Involving Operations in Sets Let be the empty set, U be the universal set, A,B,C,X be any set. 1. Xn= 2. XnU= X 3. XU=X 4. XUU=U 5. , the complement of the complement of a set is the set itself 6. (AUB)UC=Au(BUC) Associative property 7. An(BnC)=(AnB)nC Associative property 8. An(BUC)=(AnB)U(AnC) distributive property 9. AU(BnC)=(AUB)n(AUC) distributive property 10. De Morgan's Law 11. De Morgan's Law 12. 13. Exercises i. Draw a Venn diagram for each of the side (the right hand side and the left hand side of the equation) of the identities mentioned in the list of identities involving set operations. Let U= {1,2,3, . 20}, A={1,2, 3,4,5,6,7,8}, B= {2,3,4, 6,7,8,13,14,15}, C=(2,4,6, ., 18,20}, and X= (10, 11, 12, ., 20}. Illustrate the identities involving operations in sets by solving the LHS and the RHS of the equations. ii.
Identities Involving Operations in Sets Let be the empty set, U be the universal set, A,B,C,X be any set. 1. Xn= 2. XnU= X 3. XU=X 4. XUU=U 5. , the complement of the complement of a set is the set itself 6. (AUB)UC=Au(BUC) Associative property 7. An(BnC)=(AnB)nC Associative property 8. An(BUC)=(AnB)U(AnC) distributive property 9. AU(BnC)=(AUB)n(AUC) distributive property 10. De Morgan's Law 11. De Morgan's Law 12. 13. Exercises i. Draw a Venn diagram for each of the side (the right hand side and the left hand side of the equation) of the identities mentioned in the list of identities involving set operations. Let U= {1,2,3, . 20}, A={1,2, 3,4,5,6,7,8}, B= {2,3,4, 6,7,8,13,14,15}, C=(2,4,6, ., 18,20}, and X= (10, 11, 12, ., 20}. Illustrate the identities involving operations in sets by solving the LHS and the RHS of the equations. ii.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
Problem 40WE
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