association law: meaning, definition, pronunciation and examples
C1Formal, Academic, Technical
Quick answer
What does “association law” mean?
The mathematical or logical principle stating that the grouping of operations in an expression does not change the result when the operations are associative.
Audio
Pronunciation
Definition
Meaning and Definition
The mathematical or logical principle stating that the grouping of operations in an expression does not change the result when the operations are associative.
In everyday or legal contexts, can refer to a law or statute governing formal organizations like professional societies, charities, or clubs. In mathematics, it strictly refers to the property of binary operations where the grouping of operands does not affect the outcome (e.g., (a + b) + c = a + (b + c)).
Dialectal Variation
British vs American Usage
Differences
In the technical sense, usage is identical. In the legal sense, the term 'associations law' or 'law of associations' is slightly more common in British legal texts, whereas 'association law' is used in the US, but both are understood. The US may also specify 'non-profit corporation law'.
Connotations
Primarily technical or legal; no strong emotional connotations.
Frequency
Low frequency in general discourse. Significantly higher in specialized fields like mathematics, logic, computer science, and legal studies.
Grammar
How to Use “association law” in a Sentence
The [operation] obeys the association law.According to the association law, (X * Y) * Z = X * (Y * Z).This is a consequence of the association law.Vocabulary
Collocations
Examples
Examples of “association law” in a Sentence
adverb
British English
- The operators combine associatively.
adjective
British English
- The addition operation is associative.
American English
- Matrix multiplication is associative but not commutative.
Usage
Meaning in Context
Business
Rare. Could refer to the legal framework for setting up a trade association or non-profit.
Academic
Standard term in mathematics, logic, and computer science courses to describe a fundamental algebraic property.
Everyday
Extremely rare. An educated speaker might use it when explaining basic math.
Technical
Core concept in abstract algebra, programming language theory, and formal logic.
Vocabulary
Synonyms of “association law”
Strong
Neutral
Weak
Vocabulary
Antonyms of “association law”
Watch out
Common Mistakes When Using “association law”
- Using 'association law' to mean 'distributive law' (a(b+c) = ab + ac).
- Saying 'it's an association law' instead of 'the operation is associative' or 'it obeys the associative law'.
- Misspelling as 'assosiation law'.
FAQ
Frequently Asked Questions
No. The associative law is about grouping (parentheses), while the commutative law is about order (a+b = b+a). Some operations, like addition, obey both.
If you are adding up a shopping bill, it doesn't matter if you group the prices of fruits together first, then dairy, or mix them; the total sum will be the same. This demonstrates the associative law of addition.
Subtraction and division are not associative. For example, (10 - 5) - 2 = 3, but 10 - (5 - 2) = 7. The results are different.
Rarely. In a legal context, it might refer to statutes governing non-profit organizations or societies, but the precise term would more likely be 'law of associations' or 'non-profit law'. The dominant meaning is mathematical.
The mathematical or logical principle stating that the grouping of operations in an expression does not change the result when the operations are associative.
Association law is usually formal, academic, technical in register.
Association law: in British English it is pronounced /əˌsəʊ.siˈeɪ.ʃən lɔː/, and in American English it is pronounced /əˌsoʊ.siˈeɪ.ʃən lɔː/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Association is about groups. The Association Law says you can re-group your friends (the numbers/operations) without changing the total (the result).
Conceptual Metaphor
MATHEMATICAL GROUPING IS SOCIAL GROUPING (You can rearrange the members into different sub-groups, but the whole team is the same).
Practice
Quiz
In which field is the term 'association law' a fundamental technical concept?