Information and Logic

Algebra of Subsets : Operations

+ is union of sets: ∪
·is intersection of sets: ∩

Complement

Algebra of Subsets

Elements: all possible subsets of S (there are 2^{| s |} subsets)

1 is the set S
0 is the empty set
+ is union of sets
· is intersection of sets

Example:

Elements:

Complement:

Union

Intersection

Is the Algebra of Subsets Boolean?

Algebra of Subsets

Union

Intersection

Is the Algebra of Subsets Boolean?

union and intersection are commutative

Absorption Theorem

Theorem 2: