Definition and Theorem: Let * be a binary operation on a set S. If S has an identity element for *; then it is unique.

Define a binary operation on a set.

A binary operation on a set has always the identity element.

Define identity element for a binary operation defined on a set.

Define a commutative binary operation on a set.

Define an associative binary operation on a set.

Determine the total number of binary operations on the set S={1,2} having 1 as the identity element.

Let * be an associative binary operation on a set S with the identity element e in S. Then. the inverse of an invertible element is unique.

Let * be a binary operation o Q defined by a^(*)b=(ab)/(4) for all a,b in Q,find identity element in Q

Write the total number of binary operations on a set consisting of two elements.

Let S={a,b,c}. Find the total number of binary operations on S.