A binary operation in a finite set can completely be described by means of a table. This table is known as composition table. The composition table helps us to verily most of the properties satisfied by the binary operations. This table can be formed as follows:
In the above example, the first element of the first row in the body of the table, 0 is obtained by adding the first element 0 of head row and the first element 0 of the head column. Similarly the third element of 4th row (5) is obtained by adding the third element 2 of the head row and the fourth element of the head column and so on.
(1) It should be noted that the elements of the set should be written in the same order both in top border and left border of the table, while preparing the composition table.
(2) Generally a table which defines a binary operation “.” on a set is called multiplication table, when the operation is “ ” the table is called an addition fable.