There are many symmetries in the operations AND (often writtenor not written, since it is a multiplication operation) and ORshown in the following table.
These symmetries make boolean algebra easier to manipulate and boolean expression easier to simplify.
Example:
Simplify:
Expression 
Rule(s) Used 
Original Expression 

Distributive. 

Complement, Identity. 

Commutative, Distributive. 

Associative, Idempotent. 

Distributive. 

Idempotent, Identity, Distributive. 

Identity, twice. 