Boolean Algebra Proofs Postulates and Theorems (Part 2)

Boolean Algebra Postulates and Theorems (Part 2):

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Commutative Law:

x + y = y + x;
x .  y  = y . x;


Associative Law:

x + (y + z) = (x + y) + z;
x .  (y .  z) = (x  . y) .  z;


Distributive law:

x . (y + z) = x  .  y  + x  .  z;
x + (y . z) = (x + y) . (x + z);


De Morgan’s Law:

(x + y)’ = x’ .  y’;
(x .  y)’ = x’ + y’;


Absorption Law:

x + x  .  y = x;
x . (x + y) = x;


Absorption Law Proof:

x + x.y = x
L.H.S =>
= x.(1 + y)   [Distributive Law]
= x.1         [We know, x + 1 = x]
= x           [We know, x . 1 = x]
= R.H.S