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How to Prove and Apply De Morgan's Laws

De Morgan's Laws Proof and real world application.

De Morgan's Laws are transformational Rules for 2 Sets

1) Complement of the Union Equals the Intersection of the Complements

not (A or B) = not A and not B

2) Complement of the Intersection Equals the Union of the Complements

not (A and B) = not A or not B

Take 2 Sets A and B

Union = A U B ← Everything in A or B

Intersection = A ∩ B ← Everything in A and B

U = Universal Set (All possible elements in your defined universe)

Complement = A’ Everything not in A, but in the Universal Set