Discrete Mathematical Structures by Pearson

7-2 Discrete Mathematical Structures

7.2 BINARY OPERATION

If we add two integers a and b, we get another integer denoted by a + b; if we subtract b from

a, we get another integer denoted by a - b and if we multiply a and b, we get another integer

denoted by a.b. In all these three processes, there is one common property involved: given any

two integers, their product under the operation is an integer. In this case, we say that the set is

closed under the operation or closure property is satisfied or a binary operation is defined over

the set.

Definition 7.1 A map or a function o : S × S → S is called a binary operation over the set S, the

function o associates each ordered pair (a, b) in S × S with a unique element c ∈ S. The o-image

of (