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:

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.

flashcards

Question	Answer
What does it mean for a boolean operator to be associative?	It means we can group the values in any way and get the same result: A \ominus (B \ominus C) = (A \ominus B) \ominus C
Which main boolean operations are associative?	AND (A \cdot (B \cdot C) = (A \cdot B) \cdot C), OR (A + (B + C) = (A + B) + C), and XOR (A \oplus (B \oplus C) = (A \oplus B) \oplus C)
How can we rewrite an expression using an associative operator?	We can rewrite A \ominus (B \ominus C) as (A \ominus B) \ominus C