relative complement: meaning, definition, pronunciation and examples
C2/TechnicalFormal, Technical, Academic
Quick answer
What does “relative complement” mean?
In set theory, the set of all elements in one set that are not in another set.
Audio
Pronunciation
Definition
Meaning and Definition
In set theory, the set of all elements in one set that are not in another set.
The mathematical operation denoted by a backslash (A \ B) or a minus sign (A – B), meaning 'elements of A not in B'. This is also called the set difference. It is called 'relative' because the result depends on the first set relative to the second, not the universal set.
Dialectal Variation
British vs American Usage
Differences
Terminology is identical in both dialects. The symbol used (backslash or minus) is standardised globally in mathematics.
Connotations
Pure mathematical, formal, and precise in both contexts.
Frequency
Used exclusively in mathematical discourse. No significant regional frequency variation.
Grammar
How to Use “relative complement” in a Sentence
[Set A] \ [Set B] = [Result]The relative complement of [Set B] in [Set A] is...[Set A] minus [Set B]Vocabulary
Collocations
Examples
Examples of “relative complement” in a Sentence
adjective
British English
- The relative complement operation is fundamental.
- We need a relative complement view of the data.
American English
- The relative complement operation is fundamental.
- A relative complement analysis was required.
Usage
Meaning in Context
Business
Almost never used.
Academic
Used in mathematics, logic, and theoretical computer science courses and publications.
Everyday
Not used in everyday conversation.
Technical
The primary context. Used in mathematical proofs, algorithm design, and data structure definitions.
Vocabulary
Synonyms of “relative complement”
Neutral
Weak
Vocabulary
Antonyms of “relative complement”
Watch out
Common Mistakes When Using “relative complement”
- Confusing it with the absolute complement (which requires a universal set).
- Misinterpreting the order: A \ B is not the same as B \ A.
FAQ
Frequently Asked Questions
Yes, these terms are completely synonymous in set theory.
An absolute complement requires a specified universal set. The relative complement only needs two sets, and the result is 'what's in the first set but not the second'.
The most common symbol is the backslash (A \ B). A minus sign (A – B) is also frequently used.
Primarily in pure mathematics (set theory, analysis), logic, probability, and computer science (especially in algorithm design and database theory).
In set theory, the set of all elements in one set that are not in another set.
Relative complement is usually formal, technical, academic in register.
Relative complement: in British English it is pronounced /ˈrɛl.ə.tɪv ˈkɒm.plɪ.mənt/, and in American English it is pronounced /ˈrɛl.ə.t̬ɪv ˈkɑːm.plə.mənt/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of 'relative' as 'family'. In family set A, the relative complement of a subset B (e.g., the parents) is the rest of the family (the children) *relative* to the whole family.
Conceptual Metaphor
SUBTRACTION AS REMOVAL: The relative complement is like removing members of one club (Set B) from the membership list of another club (Set A).
Practice
Quiz
What does the relative complement A \ B represent?