Binary OperationConsider a nonempty set A and α function f: AxA→A is called a binary operation on A. If * is a binary operation on A, then it may be written as a*b. A binary operation can be denoted by any of the symbols +,,*,⨁,△,⊡,∨,∧ etc. The value of the binary operation is denoted by placing the operator between the two operands.Example:
NARY Operation:A function f: AxAx.............A→A is called an nary operation. Tables of Operation:Consider a nonempty finite set A= {a_{1},a_{2},a_{3},....a_{n}}. A binary operation * on A can be described by means of table as shown in fig:
The empty in the jth row and the kth column represent the elements a_{j}*a_{k}. Example: Consider the set A = {1, 2, 3} and a binary operation * on the set A defined by a * b = 2a+2b. Represent operation * as a table on A. Solution: The table of the operation is shown in fig:
Next TopicProperty of Binary Operations

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