ASSOCIATIVE LAW Meaning and
Definition
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The associative law is a fundamental principle in mathematics that governs the way in which operations can be rearranged and grouped within a set. It states that for any operation, the grouping of elements does not affect the outcome.
In more precise terms, the associative law specifies that for any three elements a, b, and c in a set, the expression (a op b) op c is equal to a op (b op c), where "op" represents any binary operation. This means that when performing a series of operations on the elements, the order in which the operations are carried out will not change the final result.
The associative law is commonly applied to addition and multiplication operations, but it can also be extended to other mathematical operations such as subtraction, division, and even set operations like intersection and union. For example, in arithmetic, the equation (2 + 3) + 4 is equal to 2 + (3 + 4), whereas in algebra, (x + y) + z is equal to x + (y + z).
This law plays a significant role in simplifying and evaluating complex expressions, as it allows mathematicians to rearrange terms and parentheses freely. Utilizing the associative law not only enhances computation efficiency but also provides a framework for expressing mathematical concepts and reasoning.
Common Misspellings for ASSOCIATIVE LAW
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Etymology of ASSOCIATIVE LAW
The term "associative law" is formed by combining two words: "associative" and "law".
The word "associative" is derived from the Latin word "associātus", which is the past participle of "associāre", meaning "to join" or "to unite". In mathematics, "associative" refers to a property that certain operations or functions possess, where the grouping of elements does not affect the result. The word "associative" itself has been in use since the early 18th century.
The word "law" comes from the Old English word "lagu", derived from the Proto-Germanic root "lagam", meaning "something that must be laid down" or "fixed decree". It dates back to before the 12th century and is used to describe a principle or rule that explains or governs some aspect of the natural or social world.
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