The symbols used are the ones AQA exam board uses: + for OR, · for AND and a bar for NOT. Other exam boards (eg OCR) may use V for OR, ^ for AND and ¬ for NOT
The order of precedence in Boolean Algebra is Brackets > Not > AND > OR
(You can sort of treat AND operations as multiplication and OR operations as addition)
| Name | Identity AQA | OCR |
|---|---|---|
| Identity Law | A + 0 = A A · 1 = A |
A v 0 = A A ^ 1 = A |
| Identity (Domination) Law | A + 1 = 1 A · 0 = 0 |
A v 1 = 1 A ^ 0 = 0 |
| Idempotent Law | A + A = A A · A = A |
A v A = A A ^ A = A |
| Complement Law | A + A = 1 A · A = 0 |
A v ¬A = 1 A ^ ¬A = 0 |
| Double Negation Law | A = A | ¬¬A = A |
| Commutative Law | A + B = B + A A · B = B · A |
A v B = B v A A ^ B = B ^ A |
| Associative Law | (A + B) + C = A + (B + C) (A · B) · C = A · (B · C) |
(A v B) v C = A v (B v C) (A ^ B) ^ C = A ^ (B ^ C) |
| Distributive Law | A · (B + C) = (A · B) + (A · C) A + (B · C) = (A + B) · (A + C) |
A ^ (B v C) = (A ^ B) v (A ^ C) A v (B ^ C) = (A v B) ^ (A v C) |
| Absorption Law | A + (A · B) = A A · (A + B) = A |
A v (A ^ B) = A A ^ (A v B) = A |
| De Morgan’s Theorems | (A · B) = A + B (A + B) = A · B |
¬(A ^ B) = ¬A v ¬B ¬(A v B) = ¬A ^ ¬B |
| Redundancy Laws (Consensus Theorem) | A + (A · B) = A + B A · (A + B) = A · B |
A v (¬A ^ B) = A v B A ^ (¬A v B) = A ^ B |