# Proving De Morgan Duality Law for Electrical Engineering

• soul
In summary, the conversation discusses unsuccessful attempts to prove De Morgan duality law in the context of electrical engineering and digital circuit design. The participants are trying to clarify the definition and scope of the duality law, specifically in relation to the statement "not (P and Q) <=> (not P) or (not Q)" and its application in digital circuit design. The conversation ends with uncertainty about the exact goal of the proof.
soul
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?

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)

## 1. What is De Morgan's Duality Law in Electrical Engineering?

De Morgan's Duality Law in Electrical Engineering states that the dual of an electrical network is obtained by interchanging the series and parallel connections of resistors, and replacing all resistors with their duals (i.e. replacing resistors with capacitors and vice versa).

## 2. Why is De Morgan's Duality Law important in Electrical Engineering?

De Morgan's Duality Law is important in Electrical Engineering because it allows for simplification of complex networks by transforming them into their duals. This makes it easier to analyze and solve problems related to electrical networks.

## 3. How do you prove De Morgan's Duality Law for electrical networks?

De Morgan's Duality Law can be proven using mathematical equations and theorems, such as Kirchhoff's Laws and Ohm's Law. By applying these equations and theorems to a given network and its dual, it can be shown that they are equivalent.

## 4. Can De Morgan's Duality Law be applied to all types of electrical networks?

Yes, De Morgan's Duality Law can be applied to all types of electrical networks, including DC and AC networks. It is a universal law that holds true for any type of network.

## 5. Are there any limitations to De Morgan's Duality Law in Electrical Engineering?

De Morgan's Duality Law is a powerful tool in Electrical Engineering, but it does have some limitations. It can only be applied to linear networks, meaning that it cannot be applied to networks with non-linear components such as diodes or transistors. Additionally, it only applies to networks with lumped elements, meaning that it cannot be applied to distributed networks like transmission lines.

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