1. Core Rules Summary
Identity & Null Laws
- A ∧ 1 ≡ A (Identity)
- A ∨ 0 ≡ A (Identity)
- A ∧ 0 ≡ 0 (Null)
- A ∨ 1 ≡ 1 (Null)
Idempotent & Inverse
- A ∧ A ≡ A (Idempotent)
- A ∨ A ≡ A (Idempotent)
- A ∧ ¬A ≡ 0 (Inverse)
- A ∨ ¬A ≡ 1 (Inverse)
Double Negation & Comm
- ¬(¬A) ≡ A (Dbl Negation)
- A ∧ B ≡ B ∧ A (Commutative)
- A ∨ B ≡ B ∨ A (Commutative)
Absorption Laws
- A ∨ (A ∧ B) ≡ A
- A ∧ (A ∨ B) ≡ A
- One variable "absorbs" the other.
Distributive Laws
- A ∧ (B ∨ C) ≡ (A ∧ B) ∨ (A ∧ C)
- A ∨ (B ∧ C) ≡ (A ∨ B) ∧ (A ∨ C)
De Morgan's Laws
- ¬(A ∧ B) ≡ ¬A ∨ ¬B
- ¬(A ∨ B) ≡ ¬A ∧ ¬B
- "Break the line, change the sign."
2. Rule Sandbox
Select a law and toggle the inputs to see it in action. Prove the equivalence to yourself!
Choose a Law
Identity Law
Left Hand Side
A ∧ 1
0
Right Hand Side
A
0
Anything ANDed with 1 remains itself.
3. Challenge Arena
Simplify the logic. Use the key for notation.
!
NOT
&
AND
|
OR
Expression to Simplify:
¬(A ∨ ¬B)