## FANDOM

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The associative property is a property of some binary operations (such as multiplication and addition in arithmetic). If an operation has the associative property, then if there is a sequence within some expression that contains two or more instances of that same operator, then the operations can be done in any order without changing the outcome. That is, the parentheses can be rearranged or the operations can be "regrouped" without changing the outcome. For example, in arithmetic, $(x+y)+z=x+(y+z).$More examples of binary operations with this property are conjunction and disjunction.

It is also a replacement rule of propositional logic that consists of the two following subrules:

$(P \wedge (Q \wedge R)) \Leftrightarrow ((P \wedge Q) \wedge R)$

$(P \vee (Q \vee R)) \Leftrightarrow ((P \vee Q) \vee R)$.

Natural Deduction Transformation Rules
Rules of Transformation