Microsoft Word - Digital Logic Design v_4_6a

2.3. Huntington’s First Set of Postulates

Postulates, Axioms or propositions are self-evident mathematical statements that are stated without
proof. The following Postulates will be used to develop Boolean Algebra.

 P1a: If X and Y are in B, then X+Y is in B
 P1b: If X and Y are in B, then X Y is in B

 P2a: There is an element 0 such that X+0 = X for every variable X.
 P2b: There is an element 1 such that X 1=X for every variable X.

 P3a: X+Y = Y+X (Commutative with respect to +)
 P3b: X Y = Y X (Commutative with respect to .)

 P4a: X+Y Z = (X+Y)(X+Z) (+ is distributive over .)

 P4b: X (Y+Z)=X Y+X Z (. is distributive over +)

 P5: For every variable X, there is a variable X such that

 a: X + X = 1


 b: X X = 0

 P6: There are at least two distinct elements in B.