With a associative operation, the brackets can be set arbitrarily. Therefore, sometimes the associative law is called "bracket law".
The associative law of an AND operation with three variables reads...
$$(A \wedge B) \wedge C = A \wedge (B \wedge C)$$
The associative law of an OR operation with three variables reads...
$$(A \vee B) \vee C = A \vee (B \vee C)$$
Comparison Arithmetic - Boolean algebra The associative law also applies to the addition and multiplication... $$(x + y) + z = x + (y + z) \quad\mbox{und}\quad (x \times y) \times z = x \times (y \times z)$$ |