Laws of Boolean Algebra

According to laws of Boolean Algebra , we use some variables i.e. (A, B, C, X, Y, Z) and Apply NOT, AND, OR operations on these variables. 

Types of Laws in Boolean Algebra 

There are several laws of Boolean algebra which are given below, let explain all equations of these laws with proof through Truth Table.
Laws of Boolean Algebra

1.Commutative Law

According to commutative law

  • Any order in which two variables are AND’ed makes the similar result always (i.e. A . B = B . A )
  • Any order in which two variables are OR’ed makes the similar result always (i.e. A + B = B + A)

Commutative Law in Boolean Algebra

2. Associative Law

  • A.(B.C) = (A.B).C = A . B . C    (AND Associate Law)
  • A + (B + C) = (A + B) + C = A + B + C    (OR Associate Law)

Associative Law (OR Operation) in Boolean Algebra



3. Distributive Law

  • A.(B + C) = (A.B) + (A.C)    (OR Distributive Law)
  • A + (B.C) = (A + B) . (A + C)    (AND Distributive Law)

Distributive Law in Boolean Algebra

4. Annulment law

According to Annulment Law

  • A variable AND’ed with 0 will always be equal to 0 (i.e. A . 0 = 0)
  • A variable OR’ed with 1 will always be equal to 1 (i.e.  A + 1 = 1)

5. Identity law

According to identity Law

  • A variable OR’ed with 0 will always be equal to that variable (i.e. A + 0 = A)
  • A variable AND’ed with 1 will always be equal to that variable (i.e. A . 1 = A)

Identity law in Boolean Algebra

6. Idempotent law

According to idempotent law

  • A variable OR’ed with itself will always be equal to that variable (i.e. A + A = A)
  • A variable AND’ed with itself will always be equal to that variable (i.e. A . A = A )

Idempotent law - Boolean Algebra

7. Complement law

According to complement law

  •   A variable AND’ed with its complement will always equal to 0.  (i.e. A . A’ = 0)  
  •  A variable OR’ed with its complement will always equal to 1. (i.e. A + A’ = 1)

Complement law in Boolean Algebra

8. Double Negation law

According to double negation law

  • Double complement of a variable will always equal to that variable. (i.e. (A’)’ =A)

9. Absorption law

  • A + (A.B) = A  (OR Absorption Law)
  • A . (A+B) = A  (AND Absorption Law)

Absorption law in Boolean Algebra

10. De Morgan’s Law

According to De Morgan’s law

  • (A.B)’ = A’ + B’
  • (A+B)’ = A’ . B’

De Morgan's Law in Boolean Algebra

Help Other’s By Sharing…

Contact Us

Burewala, Vehari, Punjab, Pakistan

cstaleem1@gmail.com

Website: CStaleem.com

Pin It on Pinterest