Boolean commutativity

If a boolean expression is commutative, it means that we can swap the order of the values and we get the same result.

We can write this for the operation \ominus as:

A \ominus B = B \ominus A

This applies for lots of operations, including:

• AND: A \cdot B = B \cdot A
• OR: A + B = B + A
• XOR: A \oplus B = B \oplus A
• NAND: \overline{A \cdot B} = \overline{B \cdot A}
• NOR: \overline{A + B} = \overline{B + A}

Links:

• booleans