Properties Related to Intersection:-Absorption, Identity, Idempotence, Commutativity, Associativity. ■ Absorption by Empty Set :
A ∩ Φ = Φ
input = Equality [Small ∩ Empty , Empty]
output = True
■ Identity :
A ∩ X = A
input = Equality [Small ∩ UnivrsalSpace , Small]
output = True
■Idempotence :
A ∩ A = A
input = Equality [Small ∩ Small , Small]
output = True
■Commutativity :
A ∩ B = B ∩ A
input = Equality [Small ∩ Big , Big ∩ Small]
output = True
■ Associativity :
A ∩ (B ∩ C) = (A ∩ B) ∩ C
input = Equality [Small ∩ (Medium ∩ Big), (Small ∩ Medium) ∩ Big]
output = True
Additional Properties :-Related to Intersection and Union
■Distributivity:
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
input = Equality [Small ∩ (Medium ∪ Big) , (Small ∩ Medium) ∪ (Small ∩ Big)]
output = True
■Distributivity:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
input = Equality [Small ∪ (Medium ∩ Big) , (Small ∪ Medium) ∩ (Small ∪ Big)]
output = True
■ Law of excluded middle :
A ∪ A' = X
input = Equality [Small ∪NotSmall , UnivrsalSpace ]
output = True
