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Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 5 - Commutative Law

Experiment 5 - The Commutative Law

The commutative law states that you can interchange A and B of the AND and OR operation, without changing the result.

AND Operation

The commutative law of an AND operation with two variables is...

$$A \wedge B = B \wedge A$$

Logical diagram commutative law of an AND operation.

Logical circuit commutative_law of an AND operation I. (Enlarge)

Logical circuit commutative_law of an AND operation II. (Enlarge)

OR Operation

The commutative law of an OR operation with two variables is...

$$A \vee B = B \vee A$$

Logical diagram commutative law of an OR operation.

Logical circuit commutative_law of an OR operation I. (Enlarge)

Logical circuit commutative_law of an OR operation II. (Enlarge)

Comparison Arithmetic - Boolean algebra

The commutative law also applies to the addition and multiplication...

$$x + y = y + x \quad\mbox{and}\quad x \times y = y \times x$$

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