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Boolean Algebra Theorems

Theorems of Boolean Algebra derived from Huntington postulates - Discussion

T1. Theorem:- x + x = x

x + x = (x + x)*1= (x + x)(x + x’)

From P8, x + xx’ = x

From duality of T1

T2. Theorem:- x*x = x

T3. Theorem:- x + 1 = 1

x + 1= (x + 1).1= (x +1)*(x + x’)

From P8, (x + 1*x’)= (x + x’)= 1

From duality of T3

T4. Theorem:- x.0 = 0

T5. x + (y + z) = (x + y) + z

From duality of T5

T6. Theorem:- x(yz) = (xy)z

T7. Theorem:- (x’)’ = x

From duality of T10

T11. Theorem:- x(x+y) = x

T8. Theorem:- (x + y)’ = x’y’

T9. Theorem:- (xy)’ = x’ + y’

T10. Theorem:- x + xy = x                          