Showcase Examples of De Morgan’s Law
Context | Example |
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Logic Puzzles | Puzzle: If it is not true that “It is raining and cold,” what can we infer? Application of De Morgan’s Law: We can infer that “It is not raining or it is not cold.” This uses De Morgan’s Law to simplify the negation of a conjunction into a disjunction. |
Programming | Scenario: Checking if a number is neither positive nor even in a programming language. Code Snippet (Pseudocode): if !(number > 0 and number % 2 == 0) can be simplified using De Morgan’s Law to if (number <= 0 or number % 2 != 0) . This demonstrates how De Morgan’s Law helps in simplifying conditional statements. |
Mathematical Proofs | Statement: Prove that the complement of the intersection of two sets A and B is equal to the union of their complements. Application of De Morgan’s Law: According to De Morgan’s Law, (A ∩ B)’ = A’ ∪ B’. This shows how De Morgan’s Law is used to simplify expressions in set theory. |
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