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प्रश्न
Define an associative binary operation on a set.
उत्तर
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:
\[\left( i \right) a * b \in A, \forall a, b \in A (\text{ Binary operation })\]
\[\left( ii \right) a * \left( b * c \right) = \left( a * b \right) * c, \forall a, b, c \text{ in A (Associative) }\]
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संबंधित प्रश्न
Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by (a, b) * (c, d) = (ac, b + ad), for all (a, b) (c, d) ∈ A.
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