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LAWS OF SETS - Coggle Diagram
LAWS OF SETS
Set Difference Laws:
A - B = A ∩ B^c
X∖Y= X ∩ Y c
(A - B) ∪ B = A ∪ B
A - (A - B) = A ∩ B
Complement Laws:
A ∪ A^c = U
A ∩ A^c = ∅
(A^c)^c = A
Idempotent Laws:
A ∪ A = A
A ∩ A = A
Identity Laws:
A ∪ ∅ = A
A ∩ U = A
Associative Laws:
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
De Morgan's Laws (THE MOST IMPORTANT):
(A ∪ B)^c = A^c ∩ B^c
(A ∩ B)^c = A^c ∪ B^c
Commutative Laws:
A ∪ B = B ∪ A
A ∩ B = B ∩ A
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
Dominanation Law
A ∩ ∅ = ∅
A ∪ U = U