Boolean Algebra

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

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

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