Associativity

A rule of inference used in prepositional logic. Written 'Assoc.' for short. It allows you to change the parenthesis for order of operations in situations when it will make no logical difference, but will allow you to manipulate statements in useful ways. To demonstrate:

(P∨{Q∨R}) = ({P∨Q}∨R)
And
(P∧{Q∧R}) = ({P∧Q}∧R)

Back up to Rules of Inference
Review your Logic symbols

A property some binary operations possess. The operation @ is associative if for all a,b,c

a@(b@c) = (a@b)@c

Examples:

• addition
• multiplication, matrix multiplication
• XOR (really an instance of addition)
• logical AND and logical OR

Non examples:

• exponentiation: (2³)⁴ = 8⁴ = 4096 < 2³⁴ = 2⁸¹ = 2417851639229258349412352.
• division: (1/2)/3 = 1/6 < 1/(2/3) = 3/2