Question

Define an associative binary operation on a set.

Answer 1

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

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