Identities Involving Operations in SetsLet Ø be the empty set, U be the universal set, A,B,C,X be any set.1. XnØ=Ø2. XnU= X3. XUØ=X4. XUU=U5. (x) = X, the complement of the complement of a set is the set itself6. (AUB)UC=AU(BUC) Associative property7. AN(BNC)=(ANB)nC Associative property8. AN(BUC)=(ANB)U(ANC) distributive property9. AU(BNC)=(AUB)N(AUC) distributive property10. (ANB)° = A° U Bº De Morgan's Law%3D11. (AUB)° = A°NB° De Morgan's Law%3D12. A-B = An B°13. АДВ %3 (А-В) U (В-А)ExercisesDraw a Venn diagram for each of the side (the right hand side and the left handside of the equation) of the identities mentioned in the list of identities involvingset operations.i.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 insets by solving the LHS and the RHS of the equations.ii.

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Identities Involving Operations in Sets Let Ø be the empty set, U be the universal set, A,B,C,X be any set. 1. XnØ=Ø 2. XnU= X 3. XUØ=X 4. XUU=U 5. (x°)° = X, 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. (ANB)° = A° U B° De Morgan's Law %3D 11. (AUB)° = A°NB° De Morgan's Law 12. A-B = A N B° 13. AAB = (A-B) U (B-A) Exercises 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. i. 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 Ø be the empty set, U be the universal set, A,B,C,X be any set. 1. XnØ=Ø 2. XnU= X 3. XUØ=X 4. XUU=U 5. (x°)° = X, 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. (ANB)° = A° U B° De Morgan's Law %3D 11. (AUB)° = A°NB° De Morgan's Law 12. A-B = A N B° 13. AAB = (A-B) U (B-A) Exercises 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. i. 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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