Week 2 - Logical Equivalence Table
1 minute read
| # |
Name |
Logical Equivalence |
| 1 |
Identity Laws |
P ∧ T ≡ P |
| |
|
P ∨ F ≡ P |
| 2 |
Domination Laws |
P ∧ F ≡ F |
| |
|
P ∨ T ≡ T |
| 3 |
Idempotent Laws |
P ∧ P ≡ P |
| |
|
P ∨ P ≡ P |
| 4 |
Double Negation Law |
¬(¬P) ≡ P |
| 5 |
Commutative Laws |
P ∧ Q ≡ Q ∧ P |
| |
|
P ∨ Q ≡ Q ∨ P |
| 6 |
Associative Laws |
(P ∧ Q) ∧ R ≡ P ∧ (Q ∧ R) |
| |
|
(P ∨ Q) ∨ R ≡ P ∨ (Q ∨ R) |
| 7 |
Distributive Laws |
P ∧ (Q ∨ R) ≡ (P ∧ Q) ∨ (P ∧ R) |
| |
|
P ∨ (Q ∧ R) ≡ (P ∨ Q) ∧ (P ∨ R) |
| 8 |
De Morgan’s Laws |
¬(P ∧ Q) ≡ ¬P ∨ ¬Q |
| |
|
¬(P ∨ Q) ≡ ¬P ∧ ¬Q |
| 9 |
Absorption Laws |
P ∧ (P ∨ Q) ≡ P |
| |
|
P ∨ (P ∧ Q) ≡ P |
| 10 |
Tautology (Implication) |
P ⟶ Q ≡ ¬P ∨ Q |
| 11 |
Equivalence (Biconditional) |
P ⟷ Q ≡ (P ⟶ Q) ∧ (Q ⟶ P) |
| 12 |
Negation Law |
P ∧ ¬P ≡ F |
| |
|
P ∨ ¬P ≡ T |
