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According to De Morgan’s Law, the intersection of two sets’ complements is the complement of their intersection, and the intersection of two sets’ complements is the complement of respective complements. These are named for De Morgan, a brilliant mathematician.
A brief outline
This law is written as (A ∪ B)’= A’ ∩ B ‘. These laws are related to the intersection and union of sets via complements in set theory. A set is a well-defined collection of objects or elements. On two sets, several operations such as complement, union, and intersection could be done.
De Morgan’s Law can be found in both set theory and boolean algebra. These rules are essential for deciphering mathematical arguments. Through complementation, a relationship between union and intersection can be constructed using these laws. The many forms of the formulas are listed below:
(A ∪ B)’ = A’ ∩ B’
(A ∩ B)’ = A’ ∪ B’
De Morgan’s Law in Practice
De Morgan’s law can be found in both elementary and Boolean algebra. This law is commonly used in most engineering industries to develop hardware and simplify operations because it helps to reduce difficult expressions.
The use of De Morgan’s law in electronic engineering for the development of logic gates can be seen. Only the NAND (AND negated) or NOR (OR negated) gates are required to produce this legal equation.
In computer programming, DE Morgan’s law is employed. This law aids in the reduction of the number of lines of logical expressions written in codes. As a result, it aids in overall code optimization.
Logic Gates are used to verify and executing DE Morgan’s First Law.
A NAND gate with inputs A and B can be used to execute the highest logic gate placement of: A.B. In the beginning, the lowermost logic gate placement inverts the two inputs, yielding A and B, which become the OR gate’s inputs. As a result, the OR gate’s output now becomes A+B.
Significance of Visualizing De Morgan’s First Law in IIT JEE exam
The Venn diagram chapter, which accounts for roughly 3.33 per cent of the total 120 marks just on JEE exam, discusses De Morgan’s law of union. Two to three questions worth approximately eight marks will be given on this topic.
Q. DeMorgan’s Theorems are a set of theorems developed by DeMorgan.
Ans: The relationship between GATES with inverted inputs and GATES with inverted outputs is usually explained using DeMorgan’s Theorems. A NAND gate is the same as a Negative-OR gate, whereas a NOR gate is the same as a Negative-AND gate.
Q. What is the significance of DeMorgan’s Theorem?
Ans: DeMorgan’s Theorem is mostly used to answer the most complex and lengthy Boolean algebra equations.
Q. How do I negate a statement using De Morgan’s Law?
Ans: Students can utilize De Morgan’s Law to negate a statement in the following way: to negate a “and” statement, the student must negate each part and replace the “and” with “or.”