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.

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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