Boolean Algebra Laws and Expressions

Start with the operations

Begin with the Boolean Algebra Laws mind map for an overview of operations in set theory and Boolean logic. It brings together intersection and AND, union and OR, and complement and negation. It also includes TRUE, FALSE, the universal set and the empty set.

Use the map to notice how the operations are presented alongside one another. Then move to the Rules of Boolean Algebra flashcards, which cover zero and unit rules, complement relations and idempotence. The cards give you expressions to work through as you study the rules.

Practice the laws and expressions

Simplifying Boolean Expressions brings general rules together with commutative, associative and distributive rules. It includes expressions using AND, OR and negation, as well as rules involving zero and one. Boolean Simplification Rules also covers general identities, distributive rules and De Morgan's laws.

After working through the cards, return to a mind map and look for the laws you have practiced. The Boolean Algebra mind map includes associative, commutative and distributive laws alongside gates, circuits and expressions. Comparing the map with the cards gives you both an overview and individual expressions to study.

Use a quiz with a map

The page lists Boolean Algebra quiz and Basic Laws for XOR. Choose a quiz after looking at the maps and flashcards, then return to the relevant resources to study the laws again. The map can help you see where a law fits, while the cards give you expressions to work through.

Explore the unit

Boolean Algebra Laws and Expressions is part of the Boolean Logic and Logic Gates unit in Computing and ICT. The Boolean Algebra map connects the laws on this page with AND, NOT, OR and NAND gates, as well as logic circuits. Pick a resource and follow the connection that is useful to your studying.