Mathematics
Boolean Algebra
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# Experiment 10 - The Associative Law

With a associative operation, the brackets can be set arbitrarily. Therefore, sometimes the associative law is called "bracket law".

## AND Operation

The associative law of an AND operation with three variables reads...

$$(A \wedge B) \wedge C = A \wedge (B \wedge C)$$

 Logic diagram associative law of an AND operation.
 Logic circuit associative law of an AND operation I. (Enlarge) Logic circuit associative law of an AND operation II. (Enlarge)

## OR Operation

The associative law of an OR operation with three variables reads...

$$(A \vee B) \vee C = A \vee (B \vee C)$$

 Logic diagram associative law of an OR operation.
 Logic circuit associative law of an OR operation I. (Enlarge) Logic circuit associative law of an OR operation II. (Enlarge)
 Comparison Arithmetic - Boolean algebra The associative law also applies to the addition and multiplication... $$(x + y) + z = x + (y + z) \quad\mbox{und}\quad (x \times y) \times z = x \times (y \times z)$$