# Boolean Laws

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

T1: Commutative Law

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

T10

(a) (b)

**T11:**

**De Morgan's Theorem**

(a) (a) (1) Algebraically: (2) Using the truth table: