How can I prove the truth of law distributive,de morgan, and arbsorption?

Distributive
X.(Y+ Z) = (X.Y)+(X.Z)
Logic Gate

Truth Table

Test on Winbreadbroad Software

Breadboard : 

Schematic :

X+(Y.Z) = (X+Y).(X+Z)
Logic Gate 

Truth Table

Test on Winbreadbroad Software

Breadboard :

Schematic :

De Morgan

(X+Y)' = X' . Y'

Logic Gate

Truth Table

Test on Winbreadbroad Software

Breadboard :

Schematic :

(XY)' = X' + Y'

Logic Gate

Truth Table

Test on Winbreadbroad Software

Breadboard :

Schematic :

Absorption

X + X.Y = X

Logic Gate

Truth Table

Test on Winbreadbroad Software

Breadboard :

Schematic :

X.(X+Y) = X

Logic Gate

Truth Table

Test on Winbreadbroad Software

Breadboard :

Schematic :