Boolean Algebra

Law	OR Form	AND Form
1. Identity Law	P + 0 = P	P ⋅ 1 = P
2. Idempotent Law	P + P = P	P ⋅ P = P
3. Commutative Law	P + Q = Q + P	P ⋅ Q = Q ⋅ P
4. Associative Law	P + (Q + R) = (P + Q) + R	P ⋅ (Q ⋅ R) = (P ⋅ Q) ⋅ R
5. Distributive Law	P + (Q ⋅ R) = (P + Q) ⋅ (P + R)	P ⋅ (Q + R) = (P ⋅ Q) + (P ⋅ R)
6. Inversion Law	(A′)′ = A	(A′)′ = A
7. De Morgan's Law	(P + Q)′ = P′ ⋅ Q′	(P ⋅ Q)′ = P′ + Q′
8. Complement Law	P + P′ = 1	P ⋅ P′ = 0
9. Domination Law	P + 1 = 1	P ⋅ 0 = 0
10. Double Negation Law	(P′)′ = P	(P′)′ = P
11. Absorption Law	P + (P ⋅ Q) = P	P ⋅ (P + Q) = P

De Morgan's Law Practice Questions

Question	Step-by-Step	Answer	Rule Used
(AB)'	(AB)' → A' + B'	A' + B'	De Morgan’s 1st Law
(A + B)'	(A + B)' → A'B'	A'B'	De Morgan’s 2nd Law
(ABC)'	(ABC)' → A' + B' + C'	A' + B' + C'	De Morgan’s 1st Law (extended)
(A + B + C)'	(A + B + C)' → A'B'C'	A'B'C'	De Morgan’s 2nd Law (extended)
((A + B)C)'	((A + B)C)' → (A + B)' + C' → A'B' + C'	A'B' + C'	De Morgan’s 1st Law + Distribution
(A + BC)'	(A + BC)' → A'(BC)' → A'(B' + C')	A'(B' + C')	De Morgan’s 2nd Law + 1st Law
(AB + C)'	(AB + C)' → (AB)'C' → (A' + B')C'	(A' + B')C'	De Morgan’s 2nd Law + 1st Law
(A' + B)'	(A' + B)' → (A')'(B')' → AB'	AB'	De Morgan’s 2nd Law
(A'B')'	(A'B')' → (A')' + (B')' → A + B	A + B	De Morgan’s 1st Law
((A + B')(C + D))'	((A + B')(C + D))' → (A + B')' + (C + D)' → (A'B) + (C'D')	(A'B) + (C'D')	De Morgan’s 1st & 2nd Law