Associative

Relating to the ability to connect or link various elements, particularly in relation to mental processes and cognitive functions. In mathematics, it describes properties of certain operations where the grouping of operands does not affect the outcome. The Associative property is fundamental in algebra and logic.

Associative meaning with examples

• The Associative property of addition states that changing the grouping of numbers does not change the sum, which simplifies complex calculations. For instance, (2 + 3) + 4 is equal to 2 + (3 + 4), both yield a total of 9, enhancing computational ease in arithmetic.
• In cognitive psychology, Associative learning occurs when an individual learns to make connections between certain stimuli and responses. For example, if a dog learns to associate the sound of a bell with receiving food, it will begin to salivate when it hears the bell, illustrating a key concept in behaviorism.
• Mathematics extensively uses the Associative property to prove the validity of expressions. For instance, in multiplication, (5 × 2) × 3 equals 5 × (2 × 3), demonstrating that the order of operations does not influence the final product, ensuring consistency in mathematical evaluations.
• The Associative nature of words in our lexicon allows for rich and complex communication. For example, when someone says 'home,' the Associative responses could include warmth, family, or comfort, showcasing how language evokes personal connections and emotional responses.