Fundamental laws of set algebra

A¯¯=A
∅¯=Ω
Ω¯=∅
A∪∅=A
A∩Ω=A
A∪Ω=Ω
 
A∩∅=A

Commutative laws

A∪B=B∪A
A∩B=B∩A

Associative laws

A∪B∪C=A∪B∪C
A∩B∩C=A∩B∩C

Distributive laws

A∪B∩C=A∪B∩A∪C
A∩B∪C=A∩B∪A∩C

Absorption laws

A∪A∩B=A
A∩A∪B=A

Idempotent laws

A∪A=A
A∩A=A

De Morgan's laws

A∪B¯=A¯∩B¯
A∩B¯=A¯∪B¯
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