1) Proof of Demorgan's Theorem for two variables.

 

Truth Table for DeMorgan's Law

X	Y	X'	Y'	(X+Y)'	X' Y'
0	0	1	1	1	1
0	1	1	0	0	0
1	0	0	1	0	0
1	1	0	0	0	0

 

Truth Table for DeMorgan's Law

X	Y	X'	Y'	(XY)'	X'+Y'
0	0	1	1	1	1
0	1	1	0	1	1
1	0	0	1	1	1
1	1	0	0	0	0

Simulation Demonstrations:

(X+Y)'



X' Y'


As you can see the two simulations above produce equal results even though they are both implimented differently. However, due to the Demorgan's theorem their implimentation doesn't matter (so long as you follow his theorem).

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