Associative law: Let s be a binary operation on a set S. a*(b*c=(a*b)*c for Va,b,c∈S Commutative law: Let *k be a binary operation on a set s. a*b=b*a for Va, bES Identity element: Let be a binary operation on a set s. An element e of s is an identity element if=e*a=afor all a ∈S Theorem 6.1: If s has an identity element, then it is unique. Associative law: Let  be a binary operation on a set S. a(bc)=(ab)c for a,b,cS  Commutative law: Let  be a binary operation on a set S. ab=ba for a,bS  Identity element: Let  be a binary operation on a set S. An element e of S is an identity element if ae=ea=a for all a S.  Theorem 6.1: If  has an identity element, then it is unique