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Boolean Algebra Theorems

T1. Theorem:-

x + x = (x + x)*1= (x + x)(x + x’)

From P8, x + xx’ = x

From duality of T1

T2. Theorem:-

T3. Theorem:-

x + 1= (x + 1).1= (x +1)*(x + x’)

From P8, (x + 1*x’)= (x + x’)= 1

From duality of T3

T4. Theorem:-

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

From duality of T5

T6. Theorem:-

T7. Theorem:-

From duality of T10

T11. Theorem:-

T8. Theorem:-

T9. Theorem:-

T10. Theorem:-