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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 [cup]  ~A = E	Complemention law
2.	A [cap]  ~A = Ø	Exclusion law

3.	A [cup]  Ø = A	Identify law
4.	A [cap]  E = A	Identify law

5.	A [cup]  E = E	Domination law
6.	A [cap]  Ø = Ø	Domination law

7.	A [cup]  A = A	Independent law
8.	A [cap]  A = A	Independent law

8.	~(~A) = A	Double complemention law

10.	A [cup]  B = B [cup]  A	Commutative law
11.	A [cap]  B = B [cap]  A	Commutative law

12.	( A [cup]  B ) [cup]  C = A [cup]  ( B [cup]  C )	Associative law
13.	( A [cap]  B ) [cap]  C = A [cap]  ( B [cap]  C )	Associative law

14.	A [cup]  ( B [cap]  C ) = ( A [cup]  B ) [cap]  ( A [cup]  C )	Distributive law
15.	A [cap]  ( B [cup]  C ) = ( A [cap]  B ) [cup]  ( A [cap]  C )	Distributive law

16.	~ (A [cup]  B ) = ~A [cap]  ~B	De Morgan's law
17.	~ (A [cap]  B ) = ~A [cup]  ~B	De Morgan's law

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Created by unroff & hp-tools. © by Hans-Peter Bischof. All Rights Reserved (1998).

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