Augustus De Morgan is the inventor of De Morgan's Law. De Morgans Law is playing a big role in digital electronics. 

There are a lot of rules in boolean algebra.

De Morgan's Law for two inputs

 
Proof:

01. 

De Morgan's Law
From the last two-column of the table we can see that rule 1 is correct.

02.

De Morgan's Law


From the last two-column of the table, we can see that rule 2 is correct.

De Morgan's Law for three inputs

De Morgan's Law
Proof:
01.

De Morgan's Law



















From the last two-column of the table, we can see that rule 1 is correct.

02.

De Morgan's Law














From the last two-column of the table, we can see that rule 2 is correct.

Use of De Morgan's Law

It is used for simplifying logical expressions.