Boolean associativity

If a booleans operator is associative, it means that we can group the values in any way and we get the same result.

For any operator \ominus which is associative, we rewrite:

A \ominus (B \ominus C) = (A \ominus B) \ominus C

The main booleans operations that are associative are:

• AND: A \cdot (B \cdot C) = (A \cdot B) \cdot C
• OR: A + (B + C) = (A + B) + C
• XOR: A \oplus (B \oplus C) = (A \oplus B) \oplus C

This means that we can group the values in any way we like when we’re using these operations, and we’ll get the same results.