The next table gives some basic identities that are useful to manipulate sets.
If E is a universal set,
E \ A = ~A
Rules Name 1. A ~A = E Complemention law 2. A ~A = Ø Exclusion law 3. A Ø = A Identify law 4. A E = A Identify law 5. A E = E Domination law 6. A Ø = Ø Domination law 7. A A = A Independent law 8. A A = A Independent law 8. ~(~A) = A Double complemention law 10. A B = B A Commutative law 11. A B = B A Commutative law 12. ( A B ) C = A ( B C ) Associative law 13. ( A B ) C = A ( B C ) Associative law 14. A ( B C ) = ( A B ) ( A C ) Distributive law 15. A ( B C ) = ( A B ) ( A C ) Distributive law 16. ~ (A B ) = ~A ~B De Morgan's law 17. ~ (A B ) = ~A ~B De Morgan's law
Last modified: 27/July/98 (12:14)