Simplifying Boolean Algebra

De Morgan's Law

"Either logical function AND or OR may be replaced by each other, given certain changes to the equation."

NOT (A OR B) = (NOT A) AND (NOT V)


Distribution

"Multiplying or factoring of an expression"

A AND (B OR C) = (A AND B) OR (A AND C)
Association

 "Allows for removal of brackets from an expression and regrouping of variables"

A OR (B OR C) = (A OR B) OR C = A OR B OR C
Commutation

"The order of application of two separate values does not matter"

A AND B = B AND A
Double Negation

 "If you reverse something twice, you end up back where you started"

THE NOT NOT OF A = A.
Absorption 

 "The second term inside the bracket can always be eliminated and 'absorbed' by the term outside the bracket if the given conditions are met"

"Rules:
  • Operators outside and inside bracket must be different.
  • The term outside bracket must also be inside the bracket."
X OR (A AND Y) = X

X AND (X OR Y) = X

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