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.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 4E: True or False? In counting combinations, order matters. In counting permutations, order matters. For...
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