Experiment 10 - The Associative Law

The associative law states that the order of execution is irrelevant for the AND and OR operations. One speaks of associative operations.

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... $$(x + y) + z = x + (y + z) \quad\mbox{und}\quad (x \times y) \times z = x \times (y \times z)$$