de morgan
Very Low (Specialist)Formal, Academic, Technical
Definition
Meaning
A surname most famously associated with Augustus De Morgan, a 19th-century British mathematician and logician. It refers primarily to him and the logical laws named after him.
Used in mathematics, logic, and computer science to refer to De Morgan's laws, which are transformation rules for manipulating logical expressions (particularly concerning the negation of conjunctions and disjunctions). Can also refer to his son, the ceramicist William De Morgan.
Linguistics
Semantic Notes
Always capitalized. In technical contexts, it functions as a proper noun used attributively (e.g., De Morgan's laws, De Morgan algebra). It is not a common English word but a named entity with specific technical application.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Pronunciation of 'Morgan' may follow general national patterns.
Connotations
Purely technical/academic; evokes logic, set theory, Boolean algebra, and mathematical history.
Frequency
Equally low frequency in both varieties, confined to specific academic/technical fields.
Vocabulary
Collocations
Grammar
Valency Patterns
[Proper Noun]'s law(s)apply [Proper Noun]via [Proper Noun]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “N/A”
Usage
Context Usage
Business
Virtually never used.
Academic
Primary context. Used in mathematics, logic, computer science, and philosophy departments when discussing propositional logic or Boolean algebra.
Everyday
Not used.
Technical
Standard term in logic design, programming (especially when simplifying conditional statements), and formal logic.
Examples
By Part of Speech
verb
British English
- N/A
American English
- N/A
adverb
British English
- N/A
American English
- N/A
adjective
British English
- The De Morgan transformation is crucial.
- It's a classic De Morgan problem.
American English
- Use the De Morgan step here.
- This is a De Morgan simplification.
Examples
By CEFR Level
- N/A
- N/A
- The programmer used De Morgan's laws to simplify the complex 'if' statement in the code.
- De Morgan was an important mathematician.
- Applying De Morgan's theorem, we can see that ¬(P ∧ Q) is logically equivalent to ¬P ∨ ¬Q.
- The proof hinges on a straightforward application of De Morgan's duality principle for sets.
Learning
Memory Aids
Mnemonic
Remember: 'De Morgan flips the sign, AND becomes OR, and OR becomes AND, when the NOT is applied to the whole gang.'
Conceptual Metaphor
LAWS ARE TRANSFORMERS (logical laws transform expressions into equivalent forms).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not translate 'De' as 'of' in this context; it is part of the surname. Transliterate as 'Де Морган'.
- The term refers to specific laws, not a general concept, so use the full name 'Законы Де Моргана' in technical contexts.
Common Mistakes
- Writing it as 'demorgan' (should be two words with a capital D and M).
- Using it as a common noun (e.g., 'a de morgan' is incorrect).
- Misapplying the laws by forgetting to negate the individual components after flipping the operator.
Practice
Quiz
De Morgan's laws are fundamental to which field?
FAQ
Frequently Asked Questions
It is a surname consisting of two words: 'De' and 'Morgan'. Both are capitalized.
Primarily in Mathematics (particularly logic and set theory), Computer Science (logic gates, programming conditions), and Philosophy (formal logic).
When you negate a bracket with AND/OR inside, flip the AND to an OR (or vice-versa) and negate each term inside. Formally: ¬(A ∧ B) = ¬A ∨ ¬B and ¬(A ∨ B) = ¬A ∧ ¬B.
No, it is exclusively a proper noun. However, one can 'apply De Morgan's laws' or 'use a De Morgan transformation'.