1. Define a binary operation on a set.
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In mathematics, a binary operation or dyadic operation is a calculation that combines two elements to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation on a set is an operation whose two domains and the codomain are the same set
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A binary operation can be considered as a function whose input is two elements of the same set S and whose output also is an element of S. ... As (a,b) is an element of the Cartesian product S×S S × S we specify a binary operation as a function from S×S S × S to S.
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