Second De Morgan’s Law in Boolean Algebra
Second De Morgan’s law states that “The complement of AND of two or more variables is equal to the OR of the complement of each variable.”
Let A and B be two variables, then mathematically Second 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.
Second 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 AND gate, and NOT gate is added to the input of OR gate, are equivalent. These two logic gate circuits are given as follows:
Second De Morgan’s Law Truth Table
The truth table for the second 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 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
De Morgan’s Law Logic
In De Morgan’s law for logic the below prepositions are tautology:
∼ (a ∧ b) ≡ ∼ a ∨ ∼ b
∼ (a ∨ b) ≡ ∼ a ∧ ∼ b
Where,
- ∧ represetns the conjuction of statemetns,
- ∨ represents the disjunction of statements,
- ~ represetns the negation of statement, and
- ≡ represents the equivalence of statements.
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