# Boolean Algebra Theorems `foundation ` of logic minimization

Theorems of Boolean Algebra are `derived from ` Huntington postulates.

T1. Theorem: x + x = x

This is how we drive it.

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

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T4. Theorem analysis:-

x.0 = 0

T5. Theorem analysis:-

x + (y + z) = (x + y) + z

... From duality of T5

T6. Theorem analysis:-

x(yz) = (xy)z

T7. Theorem analysis:-

(x’)’ = x

T8. Theorem analysis:-

(x + y)’ = x’y’
T9. Theorem analysis:-

(xy)’ = x’ + y’

T10. Theorem analysis:-

x + xy = x

... From duality of T10

T11. Theorem:-

x(x+y) = x

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