# binary operation

**binary operation** **1.** (**dyadic operation**) defined on a set *S*. A function from the domain *S *× *S* into *S* itself. Many of the everyday arithmetic and algebraic operations are binary, including the addition of two integers, the union of two sets, and the conjunction of two Boolean expressions.

Although basically functions, binary operations are usually represented using an infix notation, as in 3 + 4, *U* ∪ *V*, *P* ∧ *Q*

The operation symbol then appears between the left and right operand. A symbol, such as ◦, can be used to represent a generalized binary operation.

When the set *S* is finite, Cayley tables and sometimes truth tables are used to define the meaning of the operation.

**2.** An operation on binary operands.

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**binary operation**