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De Morgan's Laws
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws.
Interesting Facts
1. Augustus De Morgan was born in Madurai, in India in 1806.
2. Augustus De Morgan became blind in one eye a month or two after he was born.
Presentation
What are De Morgan's Laws?
De Morgan's Laws describe how mathematical statements and concepts are related through their opposites. De Morgan's Laws are also applicable in computer engineering for developing logic gates.
De Morgan's Laws
Not (A and B) is the same as Not A or Not B.
Not (A or B) is the same as Not A and Not B.
Suggested Video
Examples of use
Example 1
Use De Morgan's law on the expression NOT(A AND B AND C).
We can represent this as ¬(A Λ B Λ C) or our preferred notation
ABC
Applying the De Morgan's rule that states XY ≡ X + Y we get
ABC ≡ A + B + C
Example 2
Use De Morgan's law on the expression NOT(A OR B OR C).
We can represent this as ¬(A V B V C) or our preferred notation
A + B + C
Applying the De Morgan's rule that states X + Y ≡ X Y we get
A + B + C ≡ A B C