Proving De Morgan Duality Law for Electrical Engineering

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I had many unsuccessful attempt to prove De Morgan duality law, for the application in electrical enginnering. Is there anyone who can help me about this?
 
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If you are talking about statement[/url], isn't it enough to just prove
| not (P and Q) <=> (not P) or (not Q)
| not (P or Q) <=> (not P) and (not Q)

and if not, what exactly do you call the "de Morgan duality law"?
 
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I tried to ask the application in digital circuit design. For example, F = A + B and F^D = A.B
Isn't it duality law?
 
I don't know, I'm not into digital circuit design.
But what exactly do you want to prove? That if F is a proposition, so is F^D? (That's what I make out of this reference)
 

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