Question

Define a commutative binary operation on a set.

Answer 1

An operation * on a set A is called a commutative binary operation if and only if it is a binary operation as well as commutative, i.e. it must satisfy the following two conditions.

\[\left( i \right) a * b \in A, \forall a, b \in A (\text{ Binary operation })\]
\[\left( ii \right) a * b = b * a, \forall a, b \in A (\text{Commutaive})\]