Elementy identycznościowe:

• (X V 0 = X   - odpowiednik bramki OR)
  X + 0 = 0 + X = X (co oznacza, że:)
  0 + 0 = 0 + 0 = 0
  1 + 0 = 0 + 1 = 1
• (X ⋀ 1 = X   - odpowiednik bramki AND)
  X * 1 = 1 * X = X (co oznacza, że:)
  0 * 1 = 1 * 0 = 0
  1 * 1 = 1 * 1 = 1

Alternatywa i koniunkcja (przemienność dodawania i mnożenia)

• (X + Y = Y + X) :==: OR
  0 + 0 = 0 + 0 = 0
  0 + 1 = 1 + 0 = 1
  1 + 1 = 1 + 1 = 1
  
• (X * Y = Y * X) :==: AND
  0 * 0 = 0 * 0 = 0
  0 * 1 = 1 * 0 = 0
  1 * 1 = 1 * 1 = 1
  

Łączność (asocjacja)

• (X + Y) + Z = X + (Y + Z)
  (0 + 0) + 0 = 0 + (0 + 0) = 0
  (0 + 0) + 1 = 0 + (0 + 1) = 1
  (0 + 1) + 0 = 0 + (1 + 0) = 1
  (0 + 1) + 1 = 0 + (1 + 1) = 1
  (1 + 0) + 0 = 1 + (0 + 0) = 1
  (1 + 0) + 1 = 1 + (0 + 1) = 1
  (1 + 1) + 0 = 1 + (1 + 0) = 1
  (1 + 1) + 1 = 1 + (1 + 1) = 1
• (X * Y) * Z = X * (Y * Z)
  (0 * 0) * 0 = 0 * (0 * 0) = 0
  (0 * 0) * 1 = 0 * (0 * 1) = 0
  (0 * 1) * 0 = 0 * (1 * 0) = 0
  (0 * 1) * 1 = 0 * (1 * 1) = 0
  (1 * 0) * 0 = 1 * (0 * 0) = 0
  (1 * 0) * 1 = 1 * (0 * 1) = 0
  (1 * 1) * 0 = 1 * (1 * 0) = 0
  (1 * 1) * 1 = 1 * (1 * 1) = 1

Absorpcja (∨ == + oraz ∧ == *)

• X ∨ (X ∧ Y) = X ∧ (X ∨ Y) = X
  inny zapis:
  X + (X * Y) = X * (X + Y) = X
  0 + (0 * 0) = 0 * (0 + 0) = 0
  0 + (0 * 1) = 0 * (0 + 1) = 1
  1 + (1 * 0) = 1 * (1 + 0) = 1
  1 + (1 * 1) = 1 * (1 + 1) = 1

Dopełnienie

• X ∨ ¬X = 1 (X + ¬X = 1 )
  oraz
  X ∧ ¬X = 0 (X * ¬X = 0)
  1 + 0 = 1
  1 * 0 = 0

Rozdzielniość operatorów

• a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c) oraz a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c)
  inny zapis:
  a + (b * c) = (a + b) * (a + c) oraz a * (b + c) = (a * b) + (a * c)
  Przykład:
  0 + (0 * 0) = (0 + 0) * (0 + 0) = 0
  1 + (0 * 0) = (1+ 0) * (1 + 0) = 1
  itd.