First De Morgan’s Law in Boolean Algebra
First De Morgan’s law states that “The complement of OR of two or more variables is equal to the AND of the complement of each variable.”
Let A and B be two variables, then mathematically First De Morgan’s Law is given as:
(A + B)’ = A’ . B’
Where
- + represents the OR operator between variables,
- . represents AND operator between variables, and
- ‘ represents complement operation on variable.
First De Morgan’s Law Logic Gates
In context to logic gates and Boolean Algebra, De Morgan’s Law states that “Both the logic gate circuits i.e., NOT gate is added to the output of OR gate, and NOT gate is added to the input of AND gate, are equivalent. These two logic gate circuits are given as follows:
First De Morgan’s Law Truth Table
The truth table for first De Morgan’s Law is given as follows:
A |
B |
A + B |
(A + B)’ |
A’ |
B’ |
A’. B’ |
---|---|---|---|---|---|---|
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
De Morgan’s Law – Theorem, Proofs, Formula & Examples
De Morgan’s law is the most common law in set theory and Boolean algebra as well as set theory. In this article, we will learn about De Morgan’s law, De Morgan’s law in set theory, and De Morgan’s law in Boolean algebra along with its proofs, truth tables, and logic gate diagrams. The article also includes the solved De Morgan’s Law Example and FAQs on De Morgan’s law. Let us learn about De Morgan’s law.
Table of Content
- What is De Morgan’s Law
- De Morgan’s Law in Set Theory
- First De Morgan’s Law
- Second De Morgan’s Law
- Proof Using Algebra of Sets
- De Morgan’s Law in Boolean Algebra
- De Morgan’s Law Formula
- Solved Examples on De Morgan’s Law
- Logic Applications of De Morgan’s Law