## 4.9. ` `Basic Set Identities

The next table gives some basic identities that are useful
to manipulate sets.` `

If E is a universal set,
then
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

Created by *unroff & hp-tools.*
© by Hans-Peter Bischof. All Rights Reserved (1998).
Last modified: 27/July/98 (12:14)