# CTE Resource Center - Verso - Electronics Systems II Boolean Laws

CTE Resource Center - Verso

Virginia’s CTE Resource Center

Boolean Laws

For more on Boolean laws, go to: http://www.electronics-tutorials.ws/boolean/bool_5.html


T1: Commutative Law


(a) A + B = B + A
(b) A B = B A

T2: Associate Law

(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)

T3: Distributive Law

(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A + C)

T4: Identity Law

(a) A + A = A
(b) A A = A

T5:

(a) AB + AB =A
(b) (A + B)A + B) = A

T6 : Redundance Law

o A + A B = A
(b) A (A + B) = A

T7:

(a) 0 + A = A
(b) 0 A = 0

T8:

(a) 1 + A = 1
(b) 1 A = A

T9:
            _
(a) A + A B = A + B = 1
          _
(b) A (A +  B)  = AB

T10
:

(a) (b)

T11: De Morgan's Theorem
(a) (a) (1) Algebraically: (2) Using the truth table: