Define an associative binary operation on a set.

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Solution

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:

$(i) a * b \in A, \forall a, b \in A (Binary operation) (ii) a * (b * c) = (a * b) * c, \forall a, b, c \in A (Associative)$

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