Laws of Boolean Algebra

The Boolean algebra is governed by certain well developed rules and laws.

Commutative Lawswell-developed

• The commutative law allows change in position of AND or OR variables. There are two commutative laws.
  (i) A + B = B + A
  Thus, the order in which the variables are ORed is immaterial.
  (ii) A ⋅ B = B ⋅ A
  Thus, the order in which the variables are ANDed is immaterial.
• This law can be extended to any number of variables.

Associative Laws

• The associative law allows grouping of variables. There are two associative laws
  (i) (A + B) + C = A + (B + C)
  Thus, the way the variables are grouped and ORed is immaterial.
  (ii) (A ⋅ B) ⋅ C = A ⋅ (B ⋅ C)
  Thus, the way the variables are grouped and ANDed is immaterial.
• This law can be extended to any number of variables.

Distributive Laws

• The distributive law allows factoring or multiplying out of expressions. There are two distributive
  laws.
  (i) A(B + C) = AB + AC
  (ii) A + BC = (A + B) (A + C)
• This law is applicable for single variable as well as a combination of variables.

Idempotent Laws

• Idempotent means the same value. There are two Idempotent laws
  (i) A ⋅ A = A
  i.e., ANDing of a variable with itself is equal to that variable only.
  (ii) A + A = A
  i.e., ORing of a variable with itself is equal to that variable only.

Absorption Laws

• There are two absorption laws
  (i) A + AB = A(1 + B) = A (ii)A (A + B) = A

Involutory Law

• This law states that, for any variable ‘A’
  A = (A′)′ = A

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