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

Last modified: 27/July/98 (12:14)