Question

Definition of commutative binary operations​

Answer 1

Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set. The binary operations * on a non-empty set A are functions from A × A to A.

Answer 2

A binary operation on any non empty set is a mapping which associates with each ordered pair (a,b) of the empty set which is defined as a*b.

Property of binary operation :

Communicative property or Communicative law.

Binary operator * is called communicative if, for  every a,b belongs to S.

(where S is the empty set)

We can say,

                      a*b = b* a                                      for all a,b ∈ S

For example,

If * is a binary operator on A given by a* b = LCM (a,b)

1) If a = 5 , b = 2 , find is * communicative?

Solution :

a* b = 5* 2 = 10 ( LCM of 5,2)

b*a = 2* 5 = 10  (LCM of 2,5)

From above ,  

 a*b = b* a    ( * is communicative on A )