Commutative and Associative Binary Operations

A binary operation * on a set S is: Commutative: if a*b = b*a for all a,b in S. Associative: If (a*b)*c = a*(b*c) for all a,b,c in S. Examples: Addition is commutative and associative Division is not commutative, not associative a*b = ab + 1 is commutative, not associative Note: Commutative does NOT imply associative, and associative does NOT imply commutative. They are independent properties, and both need to be checked.