They are the names of Augustus De Morgan, who was a British mathematician in the 19th century. The set of all those elements which are either in A or in B is the union of two sets A and B.
In other we can say that the complement of the intersection of two sets A and B is equal to the union of their separate complements.
The mathematical representation of de morgan’s laws on union is:
(A∩B)’ = A’ B’
But the our focus on the de morgan’s law on intersection in digital electronics
Further in this article we will do the proof of this law as well.
And also take some questions related to this topic to understand this more easily and fast.
DE MORGAN’S THEOREMS IN BOOLEAN ALGEBRA
De Morgan’s theorem says that the boolean expressions for AND, OR and NOT using two input variables A and B gives the two sets law.
DE MORGAN’S LAW IN INTERSECTION IN DIGITAL ELECTRONICS(BOOLEAN)
This is also called the second theorem of de Morgan’s theorem.
It proves that AND’ed and negated are equivalent to the OR of complements of separate variables if the two variables are ADDed and negated.
We show A.B = A + B by using the following table .
STATEMENT OF DE MORGAN’S LAW THEOREM IN SET THEORY
Let two sets be A and B and their complements be A’ And B’ .
First law of De morgan’s says that the union of complement of the two sets A and B is equal to the intersection of their separate complements.
(A∪B)’=A’∩B’
Second law of De morgan’s says that the complement of the intersection of two sets A and B is equal to the union of their separate complements.
(A∩B)’ = A’ B’
DE MORGAN’S LAW PROOF IN SET THEORY
DE MORGAN’S LAW ON INTERSECTION IN SET THEORY
This Is also known as the Second law of de Morgan’s theorem which says that the complement of the intersection of two sets A and B is equal to the union of their separate complements. (A∩B)’ = A’ B’
PROOF OF DE MORGAN’S LAW ON INTERSECTION IN SET THEORY
EXAMPLE OF DE MORGAN’S LAW ON INTERSECTION
Example 1: Let the universal set U={2,3,4,5,12,13,17}
The two subset A={12,13,17}
B={2,3}
(A∩B)=ø
(A∩B)’= {2,3,4,5,12,13,17}
A’ B’ = {2,3,4,5,12,13,17}
Hence, (A∩B)’ = A’ B’
CONCLUSION
In this article we learn the de morgan’s theorem statement and its proof in set theory and our main focus in on the de morgan’s law on intersection we talk about the statement of
de morgan’s law on intersection and its proof in set theory as well as in boolean algebra and also do some examples so that it will clear better and solve some questions based on de morgan’s law on intersection.